Method for transmitting 4-antenna precoding matrix, user equipment and base station

ABSTRACT

Embodiments disclose a method for transmitting a 4-antenna precoding matrix, a user equipment, and a base station. The method includes determining a rank used for indicating the number of transmission layers, determining a first precoding matrix in a codebook set corresponding to the rank, determining a first PMI and a second PMI used for indicating the first precoding matrix, and sending the first PMI and the second PMI used for indicating the first precoding matrix to a base station.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. application Ser. No.14/960,100, filed on Dec. 4, 2015, which is a continuation ofInternational Application No. PCT/CN2013/076735, filed on Jun. 4, 2013.The disclosures of the aforementioned applications are herebyincorporated by reference in their entireties.

TECHNICAL FIELD

The present invention relates to the communications field, and inparticular, to a method for transmitting a 4-antenna precoding matrix, auser equipment and a base station in the communications field.

BACKGROUND

A multiple input multiple output (“MIMO” for short) radio system iscapable of obtaining diversity and an array gain by means of transmitbeamforming (“BF” for short)/precoding and receive signal combination. Asignal vector received by a typical system that uses BF or precoding maybe represented by the following equation (1):y=HVs+n  (1)where y represents the received signal vector, H represents a channelmatrix, V represents a precoding matrix, s represents a transmittedsymbol vector, and n represents measured noise.

Optimal precoding generally requires that a transmitter completely knownchannel state information (“CSI” for short). A common method is that auser equipment (“UE” for short) quantizes instantaneous CSI and feedsback the CSI to an evolved NodeB (“eNB” for short). In the release 8(R8) of an existing Long Term Evolution (“LTE” for short) system, CSIinformation fed back by the UE may include information such as a rankindicator (“RI” for short), a precoding matrix indicator (“PMI” forshort), and a channel quality indicator (“CQI” for short), where the RIand the PMI respectively indicate the number of layers and a precodingmatrix that are used. A codebook of the LTE R8 is designed mainly forsingle user MIMO (“SU-MIMO” for short), where a precoding matrix or acode word needs to satisfy an 8 phase shift keying (“8PSK” for short)restraint, which limits precision of space quantization. This causes aserious limitation to performance of a transmission manner that issensitive to space quantization precision, such as multi-user MIMO(“MU-MIMO” for short).

In order to satisfy a higher system requirement, a 3rd GenerationPartnership Project (“3GPP” for short) LTE system needs to furtherenhance performance of MU-MIMO; moreover, a coordinated multi-point(“CoMP” for short) transmission technology is further introduced intothe system. At present, the CoMP technology is based on single-cellfeedback; therefore, both the foregoing two technologies raise higherrequirements on feedback performance. Because a capacity of a feedbackchannel is limited, a size of a codebook set is also limited, whichraises higher requirements on codebook designing.

A 3GPP LTE R8 system uses a single codebook, where a precoding matrix isindicated by an RI and a PMI. With respect to a 4-antenna system,correspondences between RIs, PMIs, and code words in a codebook areshown in the following Table 1:

TABLE 1 RI PMI u_(n) 1 2 3 4 0 u₀ = [1 −1 −1 −1]^(T) W₀ ^({1}) W₀^({14})/{square root over (2)} W₀ ^({124})/{square root over (3)} W₀^({1234})/2 1 u₁ = [1 −j 1 j]^(T) W₁ ^({1}) W₁ ^({12})/{square root over(2)} W₁ ^({123})/{square root over (3)} W₁ ^({1234})/2 2 u₂ = [1 1 −11]^(T) W₂ ^({1}) W₂ ^({12})/{square root over (2)} W₂ ^({123})/{squareroot over (3)} W₂ ^({3214})/2 3 u₃ = [1 j 1 −j]^(T) W₃ ^({1}) W₃^({12})/{square root over (2)} W₃ ^({123})/{square root over (3)} W₃^({3214})/2 4 u₄ = [1 (−1 − j)/{square root over (2)} −j (1 − j)/{squareroot over (2)}]^(T) W₄ ^({1}) W₄ ^({14})/{square root over (2)} W₄^({124})/{square root over (3)} W₄ ^({1234})/2 5 u₅ = [1 (1 − j)/{squareroot over (2)} j (−1 − j)/{square root over (2)}]^(T) W₅ ^({1}) W₅^({14})/{square root over (2)} W₅ ^({124})/{square root over (3)} W₅^({1234})/2 6 u₆ = [1 (1 + j)/{square root over (2)} −j (−1 + j)/{squareroot over (2)}]^(T) W₆ ^({1}) W₆ ^({13})/{square root over (2)} W₆^({134})/{square root over (3)} W₆ ^({1324})/2 7 u₇ = [1 (−1 +j)/{square root over (2)} j (1 + j)/{square root over (2)}]^(T) W₇^({1}) W₇ ^({13})/{square root over (2)} W₇ ^({134})/{square root over(3)} W₇ ^({1324})/2 8 u₈ = [1 −1 1 1]^(T) W₈ ^({1}) W₈ ^({12})/{squareroot over (2)} W₈ ^({124})/{square root over (3)} W₈ ^({1234})/2 9 u₉ =[1 −j −1 −j]^(T) W₉ ^({1}) W₉ ^({14})/{square root over (2)} W₉^({134})/{square root over (3)} W₉ ^({1234})/2 10 u₁₀ = [1 1 1 −1]^(T)W₁₀ ^({1}) W₁₀ ^({13})/{square root over (2)} W₁₀ ^({123})/{square rootover (3)} W₁₀ ^({1324})/2 11 u₁₁ = [1 j −1 j]^(T) W₁₁ ^({1}) W₁₁^({13})/{square root over (2)} W₁₁ ^({134})/{square root over (3)} W₁₁^({1324})/2 12 u₁₂ = [1 −1 −1 1]^(T) W₁₂ ^({1}) W₁₂ ^({12})/{square rootover (2)} W₁₂ ^({123})/{square root over (3)} W₁₂ ^({1234})/2 13 u₁₃ =[1 −1 1 −1]^(T) W₁₃ ^({1}) W₁₃ ^({13})/{square root over (2)} W₁₃^({123})/{square root over (3)} W₁₃ ^({1324})/2 14 u₁₄ = [1 1 −1 −1]^(T)W₁₄ ^({1}) W₁₄ ^({13})/{square root over (2)} W₁₄ ^({123})/{square rootover (3)} W₁₄ ^({3214})/2 15 u₁₅ = [1 1 1 1]^(T) W₁₅ ^({1}) W₁₅^({12})/{square root over (2)} W₁₅ ^({123})/{square root over (3)} W₁₅^({1234})/2where W_(n) ^({s}) represents a matrix formed by a column set {s} of amatrix W_(n)=I−2u_(n)u_(n) ^(H)/u_(n) ^(H)u_(n), I is a 4×4 identitymatrix, and u_(n) is given in the foregoing Table 1.

In the codebook of the R8 system, with respect to a precoding matrixwhose rank is 1, precoding matrices whose indexes are 0 to 7 arediscrete Fourier transform (“DFT” for short) vectors, where the DFTvectors are applicable to a uniform linear array (“ULA” for short)antenna. A DFT vector indicates a Tx1 precoding matrix, and the DFTvector v generally has a form shown in equation (2):v=[1e ^(j2πm/N) . . . e ^(j2π(T-2)m/N) e ^(j2π(T-1)m/N)]  (2),

where N and m are integers, N=2^(x), where x is a nonnegative integer,that is, N is 2 raised to the power of x, and a t^(th) element of theDFT vector v is e^(j2π(t-1)m/N) (t=1, 2, . . . , T).

In a release 10 (R10) of the 3GPP LTE system, a codebook used by an8-antenna system is formed by two groups of DFT vectors ν_(m), and thetwo groups of DFT vectors have a phase difference φ_(n), where the DFTvectors ν_(m) and the phase difference are represented by the followingequation (3):ν_(m)=[1e ^(j2πm/32) e ^(j4πm/32) e ^(j6πm/32)]^(T), φ_(n) =e^(jπn/2)  (3)

The following provides a codebook structure of the 8-antenna system. Thecodebook structure is designed for a dual-polarized antenna. Table 2shows an 8-antenna codebook when a rank is 1 (that is, the number oftransmission layers is one layer), Table 3 shows the 8-antenna codebookwhen the rank is 2 (that is, the number of transmission layers is twolayers), Table 4 shows the 8-antenna codebook when the rank is 3 (thatis, the number of transmission layers is three layers), and Table 5shows the 8-antenna codebook when the rank is 4 (that is, the number oftransmission layers is four layers).

TABLE 2 i₂ i₁ 0 1 2 3 4 5 6 7 0-15 W_(2i) ₁ _(,0) ⁽¹⁾ W_(2i) ₁ _(,1) ⁽¹⁾W_(2i) ₁ _(,2) ⁽¹⁾ W_(2i) ₁ _(,3) ⁽¹⁾ W_(2i) ₁ _(+1,0) ⁽¹⁾ W_(2i) ₁_(+1,1) ⁽¹⁾ W_(2i) ₁ _(+1,2) ⁽¹⁾ W_(2i) ₁ _(+1,3) ⁽¹⁾ i₂ i₁ 8 9 10 11 1213 14 15 0-15 W_(2i) ₁ _(+2,0) ⁽¹⁾ W_(2i) ₁ _(+2,1) ⁽¹⁾ W_(2i) ₁ _(+2,2)⁽¹⁾ W_(2i) ₁ _(+2,3) ⁽¹⁾ W_(2i) ₁ _(+3,0) ⁽¹⁾ W_(2i) ₁ _(+3,1) ⁽¹⁾W_(2i) ₁ _(+3,2) ⁽¹⁾ W_(2i) ₁ _(+3,3) ⁽¹⁾ where,$W_{m,n}^{(1)} = {\frac{1}{\sqrt{8}}\begin{bmatrix}v_{m} \\{\varphi_{n}v_{m}}\end{bmatrix}}$

TABLE 3 i₂ i₁ 0 1 2 3 0-15 W_(2i) ₁ _(,2i) ₁ _(,0) ⁽²⁾ W_(2i) ₁ _(,2i) ₁_(,1) ⁽²⁾ W_(2i) ₁ _(+1,2i) ₁ _(+1,0) ⁽²⁾ W_(2i) ₁ _(+1,2i) ₁ _(+1,1)⁽²⁾ i₂ i₁ 4 5 6 7 0-15 W_(2i) ₁ _(+2,2i) ₁ _(+2,0) ⁽²⁾ W_(2i) ₁ _(+2,2i)₁ _(+2,1) ⁽²⁾ W_(2i) ₁ _(+3,2i) ₁ _(+3,0) ⁽²⁾ W_(2i) ₁ _(+3,2i) ₁_(+3,1) ⁽²⁾ i₂ i₁ 8 9 10 11 0-15 W_(2i) ₁ _(,2i) ₁ _(+1,0) ⁽²⁾ W_(2i) ₁_(,2i) ₁ _(+1,1) ⁽²⁾ W_(2i) ₁ _(+1,2i) ₁ _(+2,0) ⁽²⁾ W_(2i) ₁ _(+1,2i) ₁_(+2,1) ⁽²⁾ i₂ i₁ 12 13 14 15 0-15 W_(2i) ₁ _(,2i) ₁ _(+3,0) ⁽²⁾ W_(2i)₁ _(,2i) ₁ _(+3,1) ⁽²⁾ W_(2i) ₁ _(+1,2i) ₁ _(+3,0) ⁽²⁾ W_(2i) ₁ _(+1,2i)₁ _(+3,1) ⁽²⁾ where,$W_{m,m^{\prime},n}^{(2)} = {\frac{1}{4}\begin{bmatrix}v_{m} & v_{m^{\prime}} \\{\varphi_{n}v_{m}} & {{- \varphi_{n}}v_{m^{\prime}}}\end{bmatrix}}$

TABLE 4 i₂ i₁ 0 1 2 0-3 W_(8i) ₁ _(,8i) ₁ _(,8i) ₁ ₊₈ ⁽³⁾ W_(8i) ₁_(+8,8i) ₁ _(,8i) ₁ ₊₈ ⁽³⁾ {tilde over (W)}_(8i) ₁ _(,8i) ₁ _(+8,8i) ₁₊₈ ⁽³⁾ i₂ i₁ 3 4 5 0-3 {tilde over (W)}_(8i) ₁ _(+8,8i) ₁ _(,8i) ₁ ⁽³⁾W_(8i) ₁ _(+2,8i) ₁ _(+2,8i) ₁ ₊₁₀ ⁽³⁾ W_(8i) ₁ _(+10,8i) ₁ _(+2,8i) ₁₊₁₀ ⁽³⁾ i₂ i₁ 6 7 8 0-3 {tilde over (W)}_(8i) ₁ _(+2,8i) ₁ _(+10,8i) ₁₊₁₀ ⁽³⁾ {tilde over (W)}_(8i) ₁ _(+10,8i) ₁ _(+2,8i) ₁ ₊₂ ⁽³⁾ W_(8i) ₁_(+4,8i) ₁ _(+4,8i) ₁ ₊₁₂ ⁽³⁾ i₂ i₁ 9 10 11 0-3 W_(8i) ₁ _(+12,8i) ₁_(+4,8i) ₁ ₊₁₂ ⁽³⁾ {tilde over (W)}_(8i) ₁ _(+4,8i) ₁ _(+12,8i) ₁ ₊₁₂⁽³⁾ {tilde over (W)}_(8i) ₁ _(+12,8i) ₁ _(+4,8i) ₁ ₊₄ ⁽³⁾ i₂ i₁ 12 13 140-3 W_(8i) ₁ _(+6,8i) ₁ _(+6,8i) ₁ ₊₁₄ ⁽³⁾ W_(8i) ₁ _(+14,8i) ₁ _(+6,8i)₁ ₊₁₄ ⁽³⁾ {tilde over (W)}_(8i) ₁ _(+6,8i) ₁ _(+14,8i) ₁ ₊₁₄ ⁽³⁾ i₂ i₁15 0-3 {tilde over (W)}_(8i) ₁ _(+14,8i) ₁ _(+6,8i) ₁ ₊₆ ⁽³⁾ where,${W_{m,m^{\prime},m^{''}}^{(3)} = {\frac{1}{\sqrt{24}}\begin{bmatrix}v_{m} & v_{m^{\prime}} & v_{m^{''}} \\v_{m} & {- v_{m^{\prime}}} & {- v_{m^{''}}}\end{bmatrix}}},{{\overset{\sim}{W}}_{m,m^{\prime},m^{''}}^{(3)} = {\frac{1}{\sqrt{24}}\begin{bmatrix}v_{m} & v_{m^{\prime}} & v_{m^{''}} \\v_{m} & v_{m^{\prime}} & {- v_{m^{''}}}\end{bmatrix}}}$

TABLE 5 i₂ i₁ 0 1 2 3 0-3 W_(8i) ₁ _(,8i) ₁ _(+8,0) ⁽⁴⁾ W_(8i) ₁ _(,8i)₁ _(+8,1) ⁽⁴⁾ W_(8i) ₁ _(+2,8i) ₁ _(+10,0) ⁽⁴⁾ W_(8i) ₁ _(+2,8i) ₁_(+10,1) ⁽⁴⁾ i₂ i₁ 4 5 6 7 0-3 W_(8i) ₁ _(+4,8i) ₁ _(+12,0) ⁽⁴⁾ W_(8i) ₁_(+4,8i) ₁ _(+12,1) ⁽⁴⁾ W_(8i) ₁ _(+6,8i) ₁ _(+14,0) ⁽⁴⁾ W_(8i) ₁_(+6,8i) ₁ _(+14,1) ⁽⁴⁾ where,${W_{m,m^{\prime},n}^{(4)} = {\frac{1}{\sqrt{32}}\begin{bmatrix}v_{m} & v_{m^{\prime}} & v_{m} & v_{m^{\prime}} \\{\varphi_{n}v_{m}} & {\varphi_{n}v_{m^{\prime}}} & {{- \varphi_{n}}v_{m}} & {{- \varphi_{n}}v_{m^{\prime}}}\end{bmatrix}}},$

An index of an 8-antenna precoding matrix may be represented by a firstcodebook index i₁ and a second codebook index i₂; with respect to the8-antenna codebook whose rank is 1, both the first codebook index i₁ andthe second codebook index i₂ need to be represented by four bits. Inorder to save an overhead of a feedback resource, a PMI may berepresented by four bits. This requires that subsampling be performed onthe PMI or the 8-antenna codebook, where a sampling codebook in asubmode 2 of a physical uplink control channel (“PUCCH” for short) mode1-1 of the 8-antenna system is shown in Table 6:

TABLE 6 First Total PMI First Codebook Second PMI Second Codebook NumberRI I_(PMI1) Index i₁ I_(PMI2) Index i₂ of Bits 1 0-7 2I_(PMI1) 0-12I_(PMI2) 4 2 0-7 2I_(PMI1) 0-1 I_(PMI2) 4 3 0-1 2I_(PMI1) 0-74└I_(PMI2)/4┘ + I_(PMI2) 4 4 0-1 2I_(PMI1) 0-7 I_(PMI2) 4 5 0-3 I_(PMI1)0 0 2 6 0-3 I_(PMI1) 0 0 2 7 0-3 I_(PMI1) 0 0 2 8 0 0 0 0 0

With respect to an enhanced 4-antenna codebook, in order to improvesystem performance without increasing complexity of codebook designingand feedback, the codebook structure design solution of the 8-antennasystem may be used, and an index of a precoding matrix may also berepresented by a first codebook index i₁ and a second codebook index i₂.In order to save an overhead of a feedback resource, a PMI may also berepresented by four bits; this also requires that subsampling beperformed on the PMI or the 4-antenna codebook.

However, with respect to a latest 4-antenna codebook used by the 3GPPLTE system, when a mode is the submode 2 of the PUCCH mode 1-1, aftersubsampling is performed on a codebook according to the 8-antennasubsampling table shown in Table 6, when a rank is 1, a precoding matrixhas only two DFT vectors. However, a 4-antenna codebook of an R8 systemhas eight DFT vectors. Therefore, when a configured antenna is a uniformlinear array ULA antenna, for the enhanced 4-antenna codebook in thesubmode 2 of the PUCCH mode 1-1, precoding matrices that are applicableto the ULA antenna are less than precoding matrices of the R8 system,and therefore performance deterioration is severe.

SUMMARY

Embodiments of the present invention provide a method for transmitting a4-antenna precoding matrix, a user equipment and a base station, whichare capable of indicating more precoding matrices that are applicable toa uniform linear array antenna without changing a feedback mode orfeedback bits.

A first aspect provides a method for transmitting a 4-antenna precodingmatrix, where the method includes determining a rank used for indicatingthe number of transmission layers; determining a first precoding matrixin a codebook set corresponding to the rank, where precoding matricesincluded in the codebook set are represented by a first codebook indexand a second codebook index. The method also includes determining afirst precoding matrix indicator PMI and a second PMI used forindicating the first precoding matrix, where the first PMI and the firstcodebook index have a first correspondence, and the second PMI and thesecond codebook index have a second correspondence. The method alsoincludes sending the first PMI and the second PMI used for indicatingthe first precoding matrix to a base station, where the precodingmatrices W included in the codebook set satisfy the following equation:

W=W₁×W₂, where

${W_{1} = \begin{bmatrix}X_{n} & 0 \\0 & X_{n}\end{bmatrix}},{X_{n} = \begin{bmatrix}1 & 1 & 1 & 1 \\q_{1}^{n} & q_{1}^{n + 8} & q_{1}^{n + 16} & q_{1}^{n + 24}\end{bmatrix}},$q₁=e^(j2π/32), and n=0, 1, . . . , 15; and

the first codebook index corresponds to one value of n, and a valuerange of n is a set {0, 1, 2, 3, 4, 5, 6, 7}, {8, 9, 10, 11, 12, 13, 14,15}, {0, 2, 4, 6, 8, 10, 12, 14}, or {1, 3, 5, 7, 9, 11, 13, 15}.

With reference to the first aspect, in a first possible implementationmanner of the first aspect, when the rank is determined to be 1, W₂satisfies the following equation:

${W_{2} \in \left\{ {{\frac{1}{A}\begin{bmatrix}Y \\{{\alpha(i)}Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{j\;{\alpha(i)}Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{{- {\alpha(i)}}Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{{- j}\;{\alpha(i)}Y}\end{bmatrix}}} \right\}},$

where Yε{e₁,e₂,e₃,e₄}, α(i)=q₁ ^(2(i-1)); when Y is e₁, α(i) is α(1);when Y is e₂, α(i) is α(2); when Y is e₃, α(i) is α(3); when Y is e₄,α(i) is α(4); e_(i) represents a column vector with a dimension of 4×1,where an i^(th) element in e_(i) is 1, all other elements are 0, andiε{1, 2, 3, 4}; A is a constant.

With reference to the first aspect, in a second possible implementationmanner of the first aspect, when the rank is determined to be 2, W₂satisfies the following equation:

$\mspace{20mu}{W_{2} \in \left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}} \right\}}$(Y₁, Y₂) ∈ {(e₁, e₁), (e₂, e₂), (e₃, e₃), (e₄, e₄), (e₁, e₂), (e₂, e₃), (e₁, e₄), (e₂, e₄)};  or$W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & Y_{2}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{- Y_{1}} & Y_{2}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{- Y_{1}} & {- Y_{2}}\end{bmatrix}}} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ \left( {e_{2},e_{4}} \right) \right\}$$W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ {\left( {e_{1},e_{1}} \right),\left( {e_{2},e_{2}} \right),\left( {e_{3},e_{3}} \right),\left( {e_{4},e_{4}} \right)} \right\}$$W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{2} & {- Y_{1}}\end{bmatrix}},} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ {\left( {e_{1},e_{3}} \right),\left( {e_{2},e_{4}} \right),\left( {e_{3},e_{1}} \right),\left( {e_{4},e_{2}} \right)} \right\}$

where e_(i) represents a column vector with a dimension of 4×1, ani^(th) element in e_(i) is 1, all other elements are 0, and iε{1, 2, 3,4}; B is a constant.

With reference to the first aspect, in a third possible implementationmanner of the first aspect, a precoding matrix set corresponding to thefirst codebook index corresponding to the first PMI includes precodingmatrices U1 and U2, where the precoding matrices U1 and U2 are indicatedby the second codebook index, where:

${{U\; 1} = {\frac{1}{A}\begin{bmatrix}v \\{\beta\; v}\end{bmatrix}}},{{U\; 2} = {\frac{1}{A}\begin{bmatrix}v \\{{- \beta}\; v}\end{bmatrix}}},{v = \begin{bmatrix}1 \\q_{1}^{n + {({8n\mspace{14mu}{mod}\mspace{14mu} 32})}}\end{bmatrix}},$β=j^(└n/4┘)*α(i), i=(n mod 4)+1, α(i)=q₁ ^(2(i-1)), and A is a constant.

With reference to the first possible implementation manner of the firstaspect, in a fourth possible implementation manner of the first aspect,when the rank is determined to be 1, the precoding matrices W includedin the codebook set are determined according to Table A:

TABLE A i₂ i₁ 0 1 2 3 0-15 W_(i) ₁ _(,0) ⁽¹⁾ W_(i) ₁ _(,1) ⁽¹⁾ W_(i) ₁_(,2) ⁽¹⁾ W_(i) ₁ _(,3) ⁽¹⁾ i₂ i₁ 4 5 6 7 0-15 W_(i) ₁ _(+8,0) ⁽¹⁾ W_(i)₁ _(+8,1) ⁽¹⁾ W_(i) ₁ _(+8,2) ⁽¹⁾ W_(i) ₁ _(+8,3) ⁽¹⁾ i₂ i₁ 8 9 10 110-15 W_(i) ₁ _(+16,0) ⁽¹⁾ W_(i) ₁ _(+16,1) ⁽¹⁾ W_(i) ₁ _(+16,2) ⁽¹⁾W_(i) ₁ _(+16,3) ⁽¹⁾ i₂ i₁ 12 13 14 15 0-15 W_(i) ₁ _(+24,0) ⁽¹⁾ W_(i) ₁_(+24,1) ⁽¹⁾ W_(i) ₁ _(+24,2) ⁽¹⁾ W_(i) ₁ _(+24,3) ⁽¹⁾

where

${W_{m,k}^{(1)} = {\frac{1}{2}\begin{bmatrix}v_{m} \\{\varphi_{k}{\gamma(m)}v_{m}}\end{bmatrix}}},{{\gamma(m)} = e^{j\; 2\pi\;\frac{{({m - i_{1}})}/4}{32}}},{v_{m} = \begin{bmatrix}1 & e^{{j2}\;\pi\;{m/32}}\end{bmatrix}},$φ_(k)=e^(jπk/2), and m and k are nonnegative integers; i₁ represents thefirst codebook index; i₂ represents the second codebook index.

With reference to the second possible implementation manner of the firstaspect, in a fifth possible implementation manner of the first aspect,when the rank is determined to be 2, the precoding matrices W includedin the codebook set are determined according to Table B1 or B2:

TABLE B1 i₂ i₁ 0 1 2 3 0-15 W_(i) ₁ _(,i) ₁ _(,0) ⁽²⁾ W_(i) ₁ _(,i) ₁_(,1) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+8,0) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+8,1) ⁽²⁾ i₂i₁ 4 5 6 7 0-15 W_(i) ₁ _(+16,i) ₁ _(+16,0) ⁽²⁾ W_(i) ₁ _(+16,i) ₁_(+16,1) ⁽²⁾ W_(i) ₁ _(+24,i) ₁ _(+24,0) ⁽²⁾ W_(i) ₁ _(+24,i) ₁ _(+24,1)⁽²⁾ i₂ i₁ 8 9 10 11 0-15 W_(i) ₁ _(,i) ₁ _(+8,0) ⁽²⁾ W_(i) ₁ _(,i) ₁_(+8,1) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+16,0) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+16,1)⁽²⁾ i₂ i₁ 12 13 14 15 0-15 W_(i) ₁ _(,i) ₁ _(+24,0) ⁽²⁾ W_(i) ₁ _(,i) ₁_(+24,1) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+24,0) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+24,1)⁽²⁾

TABLE B2 i₂ i₁ 0 1 2 3 0-15 W_(i) ₁ _(,i) ₁ _(,0) ⁽²⁾ W_(i) ₁ _(,i) ₁_(,1) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+8,0) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+8,1) ⁽²⁾ i₂i₁ 4 5 6 7 0-15 W_(i) ₁ _(+16,i) ₁ _(+16,0) ⁽²⁾ W_(i) ₁ _(+16,i) ₁_(+16,1) ⁽²⁾ W_(i) ₁ _(+24,i) ₁ _(+24,0) ⁽²⁾ W_(i) ₁ _(+24,i) ₁ _(+24,1)⁽²⁾ i₂ i₁ 8 9 10 11 0-15 {tilde over (W)}_(i) ₁ _(+8,i) ₁ _(+24,0) ⁽²⁾W_(i) ₁ _(+8,i) ₁ _(+24,0) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+24,2) ⁽²⁾ {tildeover (W)}_(i) ₁ _(+8,i) ₁ _(+24,2) ⁽²⁾ i₂ i₁ 12 13 14 15 0-15

where

${W_{m,m^{\prime},k}^{(2)} = {\frac{1}{\sqrt{8}}\begin{bmatrix}v_{m} & v_{m^{\prime}} \\{\varphi_{k}v_{m}} & {{- \varphi_{k}}v_{m^{\prime}}}\end{bmatrix}}},{{\overset{\sim}{W}}_{m,m^{\prime},k}^{(2)} = {\frac{1}{\sqrt{8}}\begin{bmatrix}v_{m} & v_{m^{\prime}} \\{\varphi_{k}v_{m}} & {\varphi_{k}v_{m^{\prime}}}\end{bmatrix}}},{{\overset{\overset{\sim}{\sim}}{W}}_{m,m^{\prime},k}^{(2)} = {\frac{1}{\sqrt{8}}\begin{bmatrix}v_{m} & v_{m^{\prime}} \\{\varphi_{k}v_{m^{\prime}}} & {{- \varphi_{k}}v_{m}}\end{bmatrix}}},{v_{m} = {{\begin{bmatrix}1 & e^{{j2}\;\pi\;{m/32}}\end{bmatrix}v_{m}} = \begin{bmatrix}1 & e^{{j2}\;\pi\;{m^{\prime}/32}}\end{bmatrix}}}$φ_(k)=e^(jπk/2), and m, m′, and k are nonnegative integers; i₁represents the first codebook index; i₂ represents the second codebookindex.

With reference to the first aspect or any possible implementation mannerof the first to the fifth possible implementation manners of the firstaspect, in a sixth possible implementation manner of the first aspect,when the rank is determined to be 1, the first PMI, the second PMI, thefirst codebook index corresponding to the first PMI, and the secondcodebook index corresponding to the second PMI are determined accordingto Table C1, C2, C3, or C4:

TABLE C1 I_(PMI1) i₁ = I_(PMI1) I_(PMI2) i₂ 0 0 0 0 0 0 1 2 1 1 0 4 1 11 6 2 2 0 8 2 2 1 10 3 3 0 12 3 3 1 14 4 4 0 1 4 4 1 3 5 5 0 5 5 5 1 7 66 0 9 6 6 1 11 7 7 0 13 7 7 1 15

TABLE C2 I_(PMI1) i₁ = I_(PMI1) + 8 I_(PMI2) i₂ 0 8 0 0 0 8 1 2 1 9 0 41 9 1 6 2 10 0 8 2 10 1 10 3 11 0 12 3 11 1 14 4 12 0 1 4 12 1 3 5 13 05 5 13 1 7 6 14 0 9 6 14 1 11 7 15 0 13 7 15 1 15

TABLE C3 I_(PMI1) i₁ = 2I_(PMI1) I_(PMI2) i₂ 0 0 0 0 0 0 1 2 1 2 0 8 1 21 10 2 4 0 1 2 4 1 3 3 6 0 9 3 6 1 11 4 8 0 0 4 8 1 2 5 10 0 8 5 10 1 106 12 0 1 6 12 1 3 7 14 0 9 7 14 1 11

TABLE C4 I_(PMI1) i₁ = 2I_(PMI1) + 1 I_(PMI2) i₂ 0 1 0 4 0 1 1 6 1 3 012 1 3 1 14 2 5 0 5 2 5 1 7 3 7 0 13 3 7 1 15 4 9 0 4 4 9 1 6 5 11 0 125 11 1 14 6 13 0 5 6 13 1 7 7 15 0 13 7 15 1 15where I_(PMI1) represents the first PMI, I_(PMI2) represents the secondPMI, i₁ represents the first codebook index, and i₂ represents thesecond codebook index.

With reference to the first aspect or any possible implementation mannerof the first to the fifth possible implementation manners of the firstaspect, in a seventh possible implementation manner of the first aspect,when the rank is determined to be 2, the value range of n may be the set{0, 1, 2, 3, 4, 5, 6, 7} or {8, 9, 10, 11, 12, 13, 14, 15}.

A second aspect provides a method for transmitting a 4-antenna precodingmatrix, where the method includes determining a rank used for indicatingthe number of transmission layers; determining a value of a firstcodebook index corresponding to one precoding matrix set in a codebookset, where the codebook set corresponds to the rank, and a precodingmatrices included in the codebook set are represented by the firstcodebook index and a second codebook index. The method also includesdetermining a jointly coded value corresponding to the rank and thevalue of the first codebook index, where the jointly coded value and therank have a first correspondence, and the jointly coded value and thefirst codebook index have a second correspondence. The method alsoincludes sending the jointly coded value to a base station, where theprecoding matrices W included in the codebook set satisfy the followingequation:

W=W₁×W₂, where

${W_{1} = \begin{bmatrix}X_{n} & 0 \\0 & X_{n}\end{bmatrix}},{X_{n} = \begin{bmatrix}1 & 1 & 1 & 1 \\q_{1}^{n} & q_{1}^{n + 8} & q_{1}^{n + 16} & q_{1}^{n + 24}\end{bmatrix}},$q₁=e^(j2π/32), and n=0, 1, . . . , 15; and

the first codebook index corresponds to one value of n, and a valuerange of n is a set {0, 1, 2, 3, 4, 5, 6, 7}, {8, 9, 10, 11, 12, 13, 14,15}, {0, 2, 4, 6}, {1, 3, 5, 7}, {8, 10, 12, 14}, or {9, 11, 13, 15}.

With reference to the second aspect, in a first possible implementationmanner of the second aspect, when the rank is determined to be 1, W₂satisfies the following equation:

${W_{2} \in \left\{ {{\frac{1}{A}\begin{bmatrix}Y \\{{\alpha(i)}Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{j\;{\alpha(i)}Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{{- {\alpha(i)}}Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{{- j}\;{\alpha(i)}Y}\end{bmatrix}}} \right\}},$

where Yε{e₁,e₂,e₃,e₄}, α(i)=q₁ ^(2(i-1)); when Y is e₁, α(i) is α(1);when Y is e₂, α(i) is α(2); when Y is e₃, α(i) is α(3); when Y is e₄,α(i) is α(4); e_(i) represents a column vector with a dimension of 4×1,where an i^(th) element in e_(i) is 1, all other elements are 0, andiε{1, 2, 3, 4}; A is a constant.

With reference to the second aspect, in a second possible implementationmanner of the second aspect, when the rank is determined to be 2, W₂satisfies the following equation:

$\mspace{20mu}{W_{2} \in \left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}} \right\}}$(Y₁, Y₂) ∈ {(e₁, e₁), (e₂, e₂), (e₃, e₃), (e₄, e₄), (e₁, e₂), (e₂, e₃), (e₁, e₄), (e₂, e₄)};  or$W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & Y_{2}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{- Y_{1}} & Y_{2}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{- Y_{1}} & {- Y_{2}}\end{bmatrix}}} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ \left( {e_{2},e_{4}} \right) \right\}$$W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ {\left( {e_{1},e_{1}} \right),\left( {e_{2},e_{2}} \right),\left( {e_{3},e_{3}} \right),\left( {e_{4},e_{4}} \right)} \right\}$$W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{2} & {- Y_{1}}\end{bmatrix}},} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ {\left( {e_{1},e_{3}} \right),\left( {e_{2},e_{4}} \right),\left( {e_{3},e_{1}} \right),\left( {e_{4},e_{2}} \right)} \right\}$

where e_(i) represents a column vector with a dimension of 4×1, ani^(th) element in e_(i) is 1, all other elements are 0, and iε{1, 2, 3,4}; B is a constant.

With reference to the second aspect or either possible implementationmanner of the first to the second possible implementation manners of thesecond aspect, in a third possible implementation manner of the secondaspect, when the number of bits bearing the jointly coded value is 4,the correspondence between the jointly coded value and the rank and thecorrespondence between the jointly coded value and the first codebookindex are determined according to the following Table D:

TABLE D I_(RI/PMI1) RI i₁ 0-7 1 I_(RI/PMI1)  8-15 2 I_(RI/PMI1) − 8where I_(RI/PMI1) represents the jointly coded value, RI represents therank, and i₁ represents the first codebook index.

With reference to the second aspect or either possible implementationmanner of the first to the second possible implementation manners of thesecond aspect, in a fourth possible implementation manner of the secondaspect, when the number of bits bearing the jointly coded value is 3,the correspondence between the jointly coded value and the rank and thecorrespondence between the jointly coded value and the first codebookindex are determined according to the following Table E:

TABLE E I_(RI/PMI1) RI i₁ 0-3 1 2 × I_(RI/PMI1) 4-7 2 2 × (I_(RI/PMI1) −4)

where I_(RI/PMI1) represents the jointly coded value, RI represents therank, and represents the first codebook index.

A third aspect provides a method for transmitting a 4-antenna precodingmatrix, where the method includes: determining a rank used forindicating the number of transmission layers; determining a firstprecoding matrix in a codebook set corresponding to the rank, whereprecoding matrices included in the codebook set are represented by afirst codebook index and a second codebook index; determining a secondprecoding matrix indicator PMI used for indicating the first precodingmatrix, where the second PMI and the second codebook index have a firstcorrespondence, and for one given first codebook index, a value range ofthe second codebook index corresponding to a value range of the secondPMI is a proper subset of a value range of the second codebook index;and sending the second PMI used for indicating the first precodingmatrix to a base station, where the precoding matrices W included in thecodebook set satisfy the following equation:

W=W₁×W₂, where

${W_{1} = \begin{bmatrix}X_{n} & 0 \\0 & X_{n}\end{bmatrix}},{X_{n} = \begin{bmatrix}1 & 1 & 1 & 1 \\q_{1}^{n} & q_{1}^{n + 8} & q_{1}^{n + 16} & q_{1}^{n + 24}\end{bmatrix}},$q₁=e^(j2π/32), and n=0, 1, . . . , 15;

the first codebook index corresponds to one value of n, and a valuerange of n is a set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14,15}; and

when the rank is determined to be 2, in precoding matrix sets that aredetermined according to the first codebook index and the second codebookindex corresponding to the value range of the second PMI, a firstprecoding matrix set corresponding to a first codebook index i_(1,a) anda second precoding matrix set corresponding to a first codebook indexi_(1,a+8) are mutually exclusive, where the first codebook index i_(1,a)represents a first codebook index corresponding to n whose value is a,the first codebook index i_(1,a+8) represents a first codebook indexcorresponding to n whose value is a+8, and aε{0, 1, 2, 3, 4, 5, 6, 7}.

With reference to the third aspect, in a first possible implementationmanner of the third aspect, when the rank is determined to be 1, W₂satisfies the following equation:

${W_{2} \in \left\{ {{\frac{1}{A}\begin{bmatrix}Y \\{{\alpha(i)}Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{j\;{\alpha(i)}Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{{- {\alpha(i)}}Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{{- j}\;{\alpha(i)}Y}\end{bmatrix}}} \right\}},$

where Yε{e₁,e₂,e₃,e₄}, α(i)=q₁ ^(2(i-1)); when Y is e₁, α(i) is α(1);when Y is e₂, α(i) is α(2); when Y is e₃, α(i) is α(3); when Y is e₄,α(i) is α(4); e_(i) represents a column vector with a dimension of 4×1,where an i^(th) element in e_(i) is 1, all other elements are 0, andiε{1, 2, 3, 4}; A is a constant.

With reference to the third aspect, in a second possible implementationmanner of the third aspect, when the rank is determined to be 2, W₂satisfies the following equation:

$\mspace{20mu}{W_{2} \in \left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}} \right\}}$(Y₁, Y₂) ∈ {(e₁, e₁), (e₂, e₂), (e₃, e₃), (e₄, e₄), (e₁, e₂), (e₂, e₃), (e₁, e₄), (e₂, e₄)};  or$W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & Y_{2}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{- Y_{1}} & Y_{2}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{- Y_{1}} & {- Y_{2}}\end{bmatrix}}} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ \left( {e_{2},e_{4}} \right) \right\}$$W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ {\left( {e_{1},e_{1}} \right),\left( {e_{2},e_{2}} \right),\left( {e_{3},e_{3}} \right),\left( {e_{4},e_{4}} \right)} \right\}$$W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{2} & {- Y_{1}}\end{bmatrix}},} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ {\left( {e_{1},e_{3}} \right),\left( {e_{2},e_{4}} \right),\left( {e_{3},e_{1}} \right),\left( {e_{4},e_{2}} \right)} \right\}$

where e_(i) represents a column vector with a dimension of 4×1, ani^(th) element in e_(i) is 1, all other elements are 0, and iε{1, 2, 3,4}; B is a constant.

With reference to the third aspect or either possible implementationmanner of the first to the second possible implementation manners of thethird aspect, in a third possible implementation manner of the thirdaspect, when the rank is determined to be 2, mutual relationshipsbetween the second PMI, the first codebook index, and the secondcodebook index are determined according to Table F1 or F2:

TABLE F1 I_(PMI2) i₁ i₂ 0-3 0-7 2 × I_(PMI2)  8-15 2 × I_(PMI2) + 1

TABLE F2 I_(PMI2) i₁ i₂ 0-3 0-7 2 × I_(PMI2)  8-15 2 × I_(PMI2) + 8

where I_(PMI2) represents the second PMI, i₁ represents the firstcodebook index, and i₂ represents the second codebook index.

With reference to the third aspect or either possible implementationmanner of the first to the second possible implementation manners of thethird aspect, in a fourth possible implementation manner of the thirdaspect, when the rank is determined to be 3 or 4, the precoding matricesincluded in the codebook set corresponding to the rank are:

four precoding matrices with codebook indexes 0 to 3 in Table G; or

four precoding matrices with codebook indexes 4 to 7 in Table G; or

four precoding matrices with codebook indexes 12 to 15 in Table G,

TABLE G Codebook RI Index u_(n) 1 2 3 4 0 u₀ = [1 −1 −1 −1]^(T) W₀^({ 1 }) W₀ ^({ 14 })/{square root over (2)} W₀ ^({ 124 })/{square rootover (3)} W₀ ^({ 1234 })/2 1 u₁ = [1 −j 1 j]^(T) W₁ ^({ 1 }) W₁^({ 12 })/{square root over (2)} W₁ ^({ 123 })/{square root over (3)} W₁^({ 1234 })/2 2 u₂ = [1 1 −1 1]^(T) W₂ ^({ 1 }) W₂ ^({ 12 })/{squareroot over (2)} W₂ ^({ 123 })/{square root over (3)} W₂ ^({ 3214 })/2 3u₃ = [1 j 1 −j]^(T) W₃ ^({ 1 }) W₃ ^({ 12 })/{square root over (2)} W₃^({ 123 })/{square root over (3)} W₃ ^({ 3214 })/2 4 u₄ = [1 (−1 −j)/{square root over (2)} −j (1 − j)/{square root over (2)}]^(T) W₄^({ 1 }) W₄ ^({ 14 })/{square root over (2)} W₄ ^({ 124 })/{square rootover (3)} W₄ ^({ 1234 })/2 5 u₅ = [1 (1 − j)/{square root over (2)} j(−1 − j)/{square root over (2)}]^(T) W₅ ^({ 1 }) W₅ ^({ 14 })/{squareroot over (2)} W₅ ^({ 124 })/{square root over (3)} W₅ ^({ 1234 })/2 6u₆ = [1 (1 + j)/{square root over (2)} −j (−1 + j)/{square root over(2)}]^(T) W₆ ^({ 1 }) W₆ ^({ 13 })/{square root over (2)} W₆^({ 134 })/{square root over (3)} W₆ ^({ 1324 })/2 7 u₇ = [1 (−1 +j)/{square root over (2)} j (1 + j)/{square root over (2)}]^(T) W₇^({ 1 }) W₇ ^({ 13 })/{square root over (2)} W₇ ^({ 134 })/{square rootover (3)} W₇ ^({ 1324 })/2 8 u₈ = [1 −1 1 1]^(T) W₈ ^({ 1 }) W₈^({ 12 })/{square root over (2)} W₈ ^({ 124 })/{square root over (3)} W₈^({ 1234 })/2 9 u₉ = [1 −j −1 −j]^(T) W₉ ^({ 1 }) W₉ ^({ 14 })/{squareroot over (2)} W₉ ^({ 134 })/{square root over (3)} W₉ ^({ 1234 })/2 10u₁₀ = [1 1 1 −1]^(T) W₁₀ ^({ 1 }) W₁₀ ^({ 13 })/{square root over (2)}W₁₀ ^({ 123 })/{square root over (3)} W₁₀ ^({ 1324 })/2 11 u₁₁ = [1 j −1j]^(T) W₁₁ ^({ 1 }) W₁₁ ^({ 13 })/{square root over (2)} W₁₁^({ 134 })/{square root over (3)} W₁₁ ^({ 1324 })/2 12 u₁₂ = [1 −1 −11]^(T) W₁₂ ^({ 1 }) W₁₂ ^({ 12 })/{square root over (2)} W₁₂^({ 123 })/{square root over (3)} W₁₂ ^({ 1234 })/2 13 u₁₃ = [1 −1 1−1]^(T) W₁₃ ^({ 1 }) W₁₃ ^({ 13 })/{square root over (2)} W₁₃^({ 123 })/{square root over (3)} W₁₃ ^({ 1324 })/2 14 u₁₄ = [1 1 −1−1]^(T) W₁₄ ^({ 1 }) W₁₄ ^({ 13 })/{square root over (2)} W₁₄^({ 123 })/{square root over (3)} W₁₄ ^({ 3214 })/2 15 u₁₅ = [1 1 11]^(T) W₁₅ ^({ 1 }) W₁₅ ^({ 12 })/{square root over (2)} W₁₅^({ 123 })/{square root over (3)} W₁₅ ^({ 1234 })/2

where W_(n) ^({s}) represents a matrix formed by a column set {s} of amatrix W_(n)=I−2u_(n)u_(n) ^(H)/u_(n) ^(H)u_(n), and I is a 4×4 identitymatrix.

A fourth aspect provides a method for transmitting a 4-antenna precodingmatrix, where the method includes receiving a rank used for indicatingthe number of transmission layers, a first precoding matrix indicatorPMI, and a second PMI that are sent by a user equipment. The methodincludes determining a first precoding matrix in a codebook setcorresponding to the rank according to the first PMI and the second PMI,where precoding matrices included in the codebook set are represented bya first codebook index and a second codebook index, the first PMI andthe first codebook index have a first correspondence, and the second PMIand the second codebook index have a second correspondence, where theprecoding matrices W included in the codebook set satisfy the followingequation:

W=W₁×W₂, where

${W_{1} = \begin{bmatrix}X_{n} & 0 \\0 & X_{n}\end{bmatrix}},{X_{n} = \begin{bmatrix}1 & 1 & 1 & 1 \\q_{1}^{n} & q_{1}^{n + 8} & q_{1}^{n + 16} & q_{1}^{n + 24}\end{bmatrix}},$q₁=e^(j2π/32), and n=0, 1, . . . , 15; and

the first codebook index corresponds to one value of n, and a valuerange of n is a set {0, 1, 2, 3, 4, 5, 6, 7}, {8, 9, 10, 11, 12, 13, 14,15}, {0, 2, 4, 6, 8, 10, 12, 14}, or {1, 3, 5, 7, 9, 11, 13, 15}.

With reference to the fourth aspect, in a first possible implementationmanner of the fourth aspect, when the received rank is 1, W₂ satisfiesthe following equation:

${W_{2} \in \left\{ {{\frac{1}{A}\begin{bmatrix}Y \\{{\alpha(i)}Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{j\;{\alpha(i)}Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{{- {\alpha(i)}}Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{{- j}\;{\alpha(i)}Y}\end{bmatrix}}} \right\}},$

where Yε{e₁,e₂,e₃,e₄}, α(i)=q₁ ^(2(i-1)); when Y is e₁, α(i) is α(1);when Y is e₂, α(i) is α(2); when Y is e₃, α(i) is α(3); when Y is e₄,α(i) is α(4); e_(i) represents a column vector with a dimension of 4×1,where an i^(th) element in e_(i) is 1, all other elements are 0, andiε{1, 2, 3, 4}; A is a constant.

With reference to the fourth aspect, in a second possible implementationmanner of the fourth aspect, when the received rank is 2, W₂ satisfiesthe following equation:

$\mspace{20mu}{W_{2} \in \left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}} \right\}}$(Y₁, Y₂) ∈ {(e₁, e₁), (e₂, e₂), (e₃, e₃), (e₄, e₄), (e₁, e₂), (e₂, e₃), (e₁, e₄), (e₂, e₄)};  or$W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & Y_{2}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{- Y_{1}} & Y_{2}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{- Y_{1}} & {- Y_{2}}\end{bmatrix}}} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ \left( {e_{2},e_{4}} \right) \right\}$$W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ {\left( {e_{1},e_{1}} \right),\left( {e_{2},e_{2}} \right),\left( {e_{3},e_{3}} \right),\left( {e_{4},e_{4}} \right)} \right\}$$W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{2} & {- Y_{1}}\end{bmatrix}},} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ {\left( {e_{1},e_{3}} \right),\left( {e_{2},e_{4}} \right),\left( {e_{3},e_{1}} \right),\left( {e_{4},e_{2}} \right)} \right\}$

where e_(i) represents a column vector with a dimension of 4×1, ani^(th) element in e_(i) is 1, all other elements are 0, and iε{1, 2, 3,4}; B is a constant.

With reference to the fourth aspect, in a third possible implementationmanner of the fourth aspect, a precoding matrix set corresponding to thefirst codebook index corresponding to the first PMI includes precodingmatrices U1 and U2, where the precoding matrices U1 and U2 are indicatedby the second codebook index, where:

${{U\; 1} = {\frac{1}{A}\begin{bmatrix}v \\{\beta\; v}\end{bmatrix}}},{{U\; 2} = {\frac{1}{A}\begin{bmatrix}v \\{{- \beta}\; v}\end{bmatrix}}},{v = \begin{bmatrix}1 \\q_{1}^{n + {({8n\mspace{14mu}{mod}\mspace{14mu} 32})}}\end{bmatrix}},$β=j^(└n/4┘)*α(i), i=(n mod 4)+1, α(i)=q₁ ^(2(i-1)), and A is a constant.

With reference to the first possible implementation manner of the fourthaspect, in a fourth possible implementation manner of the fourth aspect,when the received rank is 1, the precoding matrices W included in thecodebook set are determined according to Table A:

TABLE A i₂ i₁ 0 1 2 3 0-15 W_(i) ₁ _(,0) ⁽¹⁾ W_(i) ₁ _(,1) ⁽¹⁾ W_(i) ₁_(,2) ⁽¹⁾ W_(i) ₁ _(,3) ⁽¹⁾ i₂ i₁ 4 5 6 7 0-15 W_(i) ₁ _(+8,0) ⁽¹⁾ W_(i)₁ _(+8,1) ⁽¹⁾ W_(i) ₁ _(+8,2) ⁽¹⁾ W_(i) ₁ _(+8,3) ⁽¹⁾ i₂ i₁ 8 9 10 110-15 W_(i) ₁ _(+16,0) ⁽¹⁾ W_(i) ₁ _(+16,1) ⁽¹⁾ W_(i) ₁ _(+16,2) ⁽¹⁾W_(i) ₁ _(+16,3) ⁽¹⁾ i₂ i₁ 12 13 14 15 0-15 W_(i) ₁ _(+24,0) ⁽¹⁾ W_(i) ₁_(+24,1) ⁽¹⁾ W_(i) ₁ _(+24,2) ⁽¹⁾ W_(i) ₁ _(+24,3) ⁽¹⁾

where

${W_{m,k}^{(1)} = {\frac{1}{2}\begin{bmatrix}v_{m} \\{\varphi_{k}{\gamma(m)}v_{m}}\end{bmatrix}}},{{\gamma(m)} = e^{j\; 2\pi\frac{{({m - i_{1}})}/4}{32}}},{v_{m} = \begin{bmatrix}1 & e^{j\; 2\pi\;{m/32}}\end{bmatrix}},$φ_(k)=e^(jπk/2), and m and k are nonnegative integers; i₁ represents thefirst codebook index; i₂ represents the second codebook index.

With reference to the second possible implementation manner of thefourth aspect, in a fifth possible implementation manner of the fourthaspect, when the received rank is 2, the precoding matrices W includedin the codebook set are determined according to Table B1 or B2:

TABLE B1 i₂ i₁ 0 1 2 3 0-15 W_(i) ₁ _(,i) ₁ _(,0) ⁽²⁾ W_(i) ₁ _(,i) ₁_(,1) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+8,0) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+8,1) ⁽²⁾ i₂i₁ 4 5 6 7 0-15 W_(i) ₁ _(+16,i) ₁ _(+16,0) ⁽²⁾ W_(i) ₁ _(+16,i) ₁_(+16,1) ⁽²⁾ W_(i) ₁ _(+24,i) ₁ _(+24,0) ⁽²⁾ W_(i) ₁ _(+24,i) ₁ _(+24,1)⁽²⁾ i₂ i₁ 8 9 10 11 0-15 W_(i) ₁ _(,i) ₁ _(+8,0) ⁽²⁾ W_(i) ₁ _(,i) ₁_(+8,1) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+16,0) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+16,1)⁽²⁾ i₂ i₁ 12 13 14 15 0-15 W_(i) ₁ _(,i) ₁ _(+24,0) ⁽²⁾ W_(i) ₁ _(,i) ₁_(+24,1) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+24,0) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+24,1)⁽²⁾

TABLE B2 i₂ i₁ 0 1 2 3 0-15 W_(i) ₁ _(,i) ₁ _(,0) ⁽²⁾ W_(i) ₁ _(,i) ₁_(,1) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+8,0) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+8,1) ⁽²⁾ i₂i₁ 4 5 6 7 0-15 W_(i) ₁ _(+16,i) ₁ _(+16,0) ⁽²⁾ W_(i) ₁ _(+16,i) ₁_(+16,1) ⁽²⁾ W_(i) ₁ _(+24,i) ₁ _(+24,0) ⁽²⁾ W_(i) ₁ _(+24,i) ₁ _(+24,1)⁽²⁾ i₂ i₁ 8 9 10 11 0-15 {tilde over (W)}_(i) ₁ _(+8,i) ₁ _(+24,0) ⁽²⁾W_(i) ₁ _(+8,i) ₁ _(+24,0) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+24,2) ⁽²⁾ {tildeover (W)}_(i) ₁ _(+8,i) ₁ _(+24,2) ⁽²⁾ i₂ i₁ 12 13 14 15 0-15

where

${W_{m,m^{\prime},k}^{(2)} = {\frac{1}{\sqrt{8}}\begin{bmatrix}v_{m} & v_{m^{\prime}} \\{\varphi_{k}v_{m}} & {{- \varphi_{k}}v_{m^{\prime}}}\end{bmatrix}}},{{\overset{\sim}{W}}_{m,m^{\prime},k}^{(2)} = {\frac{1}{\sqrt{8}}\begin{bmatrix}v_{m} & v_{m^{\prime}} \\{\varphi_{k}v_{m}} & {\varphi_{k}v_{m^{\prime}}}\end{bmatrix}}},{{\overset{\overset{\sim}{\sim}}{W}}_{m,m^{\prime},k}^{(2)} = {\frac{1}{\sqrt{8}}\begin{bmatrix}v_{m} & v_{m^{\prime}} \\{\varphi_{k}v_{m^{\prime}}} & {{- \varphi_{k}}v_{m}}\end{bmatrix}}},{v_{m} = \begin{bmatrix}1 & e^{j\; 2\pi\;{m/32}}\end{bmatrix}},{v_{m^{\prime}} = \begin{bmatrix}1 & e^{j\; 2\pi\;{m^{\prime}/32}}\end{bmatrix}},$φ_(k)=e^(jπk/2), and m, m′, and k are nonnegative integers; i₁represents the first codebook index; i₂ represents the second codebookindex.

With reference to the fourth aspect or any possible implementationmanner of the first to the fifth possible implementation manners of thefourth aspect, in a sixth possible implementation manner of the fourthaspect, when the received rank is 1, the first PMI, the second PMI, thefirst codebook index corresponding to the first PMI, and the secondcodebook index corresponding to the second PMI are determined accordingto Table C1, C2, C3, or C4:

TABLE C1 I_(PMI1) i₁ = I_(PMI1) I_(PMI2) i₂ 0 0 0 0 0 0 1 2 1 1 0 4 1 11 6 2 2 0 8 2 2 1 10 3 3 0 12 3 3 1 14 4 4 0 1 4 4 1 3 5 5 0 5 5 5 1 7 66 0 9 6 6 1 11 7 7 0 13 7 7 1 15

TABLE C2 I_(PMI1) i₁ = I_(PMI1) + 8 I_(PMI2) i₂ 0 8 0 0 0 8 1 2 1 9 0 41 9 1 6 2 10 0 8 2 10 1 10 3 11 0 12 3 11 1 14 4 12 0 1 4 12 1 3 5 13 05 5 13 1 7 6 14 0 9 6 14 1 11 7 15 0 13 7 15 1 15

TABLE C3 I_(PMI1) i₁ = 2I_(PMI1) I_(PMI2) i₂ 0 0 0 0 0 0 1 2 1 2 0 8 1 21 10 2 4 0 1 2 4 1 3 3 6 0 9 3 6 1 11 4 8 0 0 4 8 1 2 5 10 0 8 5 10 1 106 12 0 1 6 12 1 3 7 14 0 9 7 14 1 11

TABLE C4 I_(PMI1) i₁ = 2I_(PMI1) + 1 I_(PMI2) i₂ 0 1 0 4 0 1 1 6 1 3 012 1 3 1 14 2 5 0 5 2 5 1 7 3 7 0 13 3 7 1 15 4 9 0 4 4 9 1 6 5 11 0 125 11 1 14 6 13 0 5 6 13 1 7 7 15 0 13 7 15 1 15

where I_(PMI1) represents the first PMI, I_(PM2) represents the secondPMI, i₁ represents the first codebook index, and i₂ represents thesecond codebook index.

With reference to the fourth aspect or any possible implementationmanner of the first to the fifth possible implementation manners of thefourth aspect, in a seventh possible implementation manner of the fourthaspect, when the received rank is 2, the value range of n may be the set{0, 1, 2, 3, 4, 5, 6, 7} or {8, 9, 10, 11, 12, 13, 14, 15}.

A fifth aspect provides a method for transmitting a 4-antenna precodingmatrix, where the method includes receiving a jointly coded value sentby a user equipment. The method also includes determining a value of afirst codebook index and a rank used for indicating the number oftransmission layers according to the jointly coded value, acorrespondence between the jointly coded value and the rank and acorrespondence between the jointly coded value and the first codebookindex, where the value of the first codebook index corresponds to oneprecoding matrix set in a codebook set, the codebook set corresponds tothe rank, precoding matrices included in the codebook set arerepresented by the first codebook index and a second codebook index, andthe precoding matrices W included in the codebook set satisfy thefollowing equation:

W=W₁×W₂, where

${W_{1} = \begin{bmatrix}X_{n} & 0 \\0 & X_{n}\end{bmatrix}},{X_{n} = \begin{bmatrix}1 & 1 & 1 & 1 \\q_{1}^{n} & q_{1}^{n + 8} & q_{1}^{n + 16} & q_{1}^{n + 24}\end{bmatrix}},$q₁=e^(j2π/32), and n=0, 1, . . . , 15; and

the first codebook index corresponds to one value of n, and a valuerange of n is a set {0, 1, 2, 3, 4, 5, 6, 7}, {8, 9, 10, 11, 12, 13, 14,15}, {0, 2, 4, 6}, {1, 3, 5, 7}, {8, 10, 12, 14}, or {9, 11, 13, 15}.

With reference to the fifth aspect, in a first possible implementationmanner of the fifth aspect, when the rank is determined to be 1, W₂satisfies the following equation:

${W_{2} \in \left\{ {{\frac{1}{A}\begin{bmatrix}Y \\{{\alpha(i)}Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{j\;{\alpha(i)}Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{{- {\alpha(i)}}Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{{- j}\;{\alpha(i)}Y}\end{bmatrix}}} \right\}},$

where Yε{e₁,e₂,e₃,e₄}, α(i)=q₁ ^(2(i-1)); when Y is e₁, α(i) is α(1);when Y is e₂, α(i) is α(2); when Y is e₃, α(i) is α(3); when Y is e₄,α(i) is α(4); e_(i) represents a column vector with a dimension of 4×1,where an i^(th) element in e_(i) is 1, all other elements are 0, andiε{1, 2, 3, 4}; A is a constant.

With reference to the fifth aspect, in a second possible implementationmanner of the fifth aspect, when the rank is determined to be 2, W₂satisfies the following equation:

$\mspace{20mu}{W_{2} \in \left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}} \right\}}$(Y₁, Y₂) ∈ {(e₁, e₁), (e₂, e₂), (e₃, e₃), (e₄, e₄), (e₁, e₂), (e₂, e₃), (e₁, e₄), (e₂, e₄)};  or$W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & Y_{2}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{- Y_{1}} & Y_{2}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{- Y_{1}} & {- Y_{2}}\end{bmatrix}}} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ \left( {e_{2},e_{4}} \right) \right\}$$W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ {\left( {e_{1},e_{1}} \right),\left( {e_{2},e_{2}} \right),\left( {e_{3},e_{3}} \right),\left( {e_{4},e_{4}} \right)} \right\}$$W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{2} & {- Y_{1}}\end{bmatrix}},} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ {\left( {e_{1},e_{3}} \right),\left( {e_{2},e_{4}} \right),\left( {e_{3},e_{1}} \right),\left( {e_{4},e_{2}} \right)} \right\}$

where e_(i) represents a column vector with a dimension of 4×1, ani^(th) element in e_(i) is 1, all other elements are 0, and iε{1, 2, 3,4}; B is a constant.

With reference to the fifth aspect or either possible implementationmanner of the first to the second possible implementation manners of thefifth aspect, in a third possible implementation manner of the fifthaspect, when the number of bits bearing the jointly coded value is 4,the correspondence between the jointly coded value and the rank and thecorrespondence between the jointly coded value and the first codebookindex are determined according to the following Table D:

TABLE D I_(RI/PMI1) RI i₁ 0-7 1 I_(RI/PMI1)  8-15 2 I_(RI/PMI1) − 8

where I_(RI/PMI1) represents the jointly coded value, RI represents therank, and i₁ represents the first codebook index.

With reference to the fifth aspect or either possible implementationmanner of the first to the second possible implementation manners of thefifth aspect, in a fourth possible implementation manner of the fifthaspect, when the number of bits bearing the jointly coded value is 3,the correspondence between the jointly coded value and the rank and thecorrespondence between the jointly coded value and the first codebookindex are determined according to the following Table E:

TABLE E I_(RI/PMI1) RI i₁ 0-3 1 2 × I_(RI/PMI1) 4-7 2 2 × (I_(RI/PMI1) −4)

where I_(RI/PMI1) represents the jointly coded value, RI represents therank, and i₁ represents the first codebook index.

A sixth aspect provides a method for transmitting a 4-antenna precodingmatrix, where the method includes receiving a second precoding matrixindicator PMI, a first codebook index, and a rank used for indicatingthe number of transmission layers that are sent by a user equipment. Themethod includes determining a first precoding matrix in a codebook setcorresponding to the rank according to the second PMI and the firstcodebook index, where precoding matrices included in the codebook setare represented by the first codebook index and a second codebook index,the second PMI and the second codebook index have a firstcorrespondence, and for one given first codebook index, a value range ofthe second codebook index corresponding to a value range of the secondPMI is a proper subset of a value range of the second codebook index,where the precoding matrices W included in the codebook set satisfy thefollowing equation:

W=W₁×W₂, where

${W_{1} = \begin{bmatrix}X_{n} & 0 \\0 & X_{n}\end{bmatrix}},{X_{n} = \begin{bmatrix}1 & 1 & 1 & 1 \\q_{1}^{n} & q_{1}^{n + 8} & q_{1}^{n + 16} & q_{1}^{n + 24}\end{bmatrix}},$q₁=e^(j2π/32), and n=0, 1, . . . , 15;

the first codebook index corresponds to one value of n, and a valuerange of n is a set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14,15}; and when the received rank is 2, in precoding matrix sets that aredetermined according to the first codebook index and the second codebookindex corresponding to the value range of the second PMI, a firstprecoding matrix set corresponding to a first codebook index i_(1,a) anda second precoding matrix set corresponding to a first codebook indexi_(1,a+8) are mutually exclusive, where the first codebook index i_(1,a)represents a first codebook index corresponding to n whose value is a,the first codebook index i_(1,a+8) represents a first codebook indexcorresponding to n whose value is a+8, and aε{0, 1, 2, 3, 4, 5, 6, 7}.

With reference to the sixth aspect, in a first possible implementationmanner of the sixth aspect, when the received rank is 1, W₂ satisfiesthe following equation:

${W_{2} \in \left\{ {{\frac{1}{A}\begin{bmatrix}Y \\{{\alpha(i)}Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{j\;{\alpha(i)}Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{{- {\alpha(i)}}Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{{- j}\;{\alpha(i)}Y}\end{bmatrix}}} \right\}},$

where Yε{e₁,e₂,e₃,e₄}, α(i)=q₁ ^(2(i-1)); when Y is e₁, α(i) is α(1);when Y is e₂, α(i) is α(2); when Y is e₃, α(i) is α(3); when Y is e₄,α(i) is α(4); e_(i) represents a column vector with a dimension of 4×1,where an i^(th) element in e_(i) is 1, all other elements are 0, andiε{1, 2, 3, 4}; A is a constant.

With reference to the sixth aspect, in a second possible implementationmanner of the sixth aspect, when the received rank is 2, W₂ satisfiesthe following equation:

$\mspace{20mu}{W_{2} \in \left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}} \right\}}$(Y₁, Y₂) ∈ {(e₁, e₁), (e₂, e₂), (e₃, e₃), (e₄, e₄), (e₁, e₂), (e₂, e₃), (e₁, e₄), (e₂, e₄)};  or$W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & Y_{2}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{- Y_{1}} & Y_{2}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{- Y_{1}} & {- Y_{2}}\end{bmatrix}}} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ \left( {e_{2},e_{4}} \right) \right\}$$W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ {\left( {e_{1},e_{1}} \right),\left( {e_{2},e_{2}} \right),\left( {e_{3},e_{3}} \right),\left( {e_{4},e_{4}} \right)} \right\}$$W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{2} & {- Y_{1}}\end{bmatrix}},} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ {\left( {e_{1},e_{3}} \right),\left( {e_{2},e_{4}} \right),\left( {e_{3},e_{1}} \right),\left( {e_{4},e_{2}} \right)} \right\}$

where e_(i) represents a column vector with a dimension of 4×1, ani^(th) element in e_(i) is 1, all other elements are 0, and iε{1, 2, 3,4}; B is a constant.

With reference to the sixth aspect or either possible implementationmanner of the first to the second possible implementation manners of thesixth aspect, in a third possible implementation manner of the sixthaspect, when the received rank is 2, mutual relationships between thesecond PMI, the first codebook index, and the second codebook index aredetermined according to Table F1 or F2:

TABLE F1 I_(PMI2) i₁ i₂ 0-3 0-7 2 × I_(PMI2)  8-15 2 × I_(PMI2) + 1

TABLE F2 I_(PMI2) i₁ i₂ 0-3 0-7 2 × I_(PMI2)  8-15 2 × I_(PMI2) + 8

where I_(PMI2) represents the second PMI, i₁ represents the firstcodebook index, and i₂ represents the second codebook index.

With reference to the sixth aspect or either possible implementationmanner of the first to the second possible implementation manners of thesixth aspect, in a fourth possible implementation manner of the sixthaspect, when the received rank is 3 or 4, the precoding matricesincluded in the codebook set corresponding to the rank are:

four precoding matrices with codebook indexes 0 to 3 in Table G; or

four precoding matrices with codebook indexes 4 to 7 in Table G; or

four precoding matrices with codebook indexes 12 to 15 in Table G,

TABLE G Codebook RI Index u_(n) 1 2 3 4 0 u₀ = [1 −1 −1 −1]^(T) W₀^({1}) W₀ ^({14})/{square root over (2)} W₀ ^({124})/{square root over(3)} W₀ ^({1234})/2 1 u₁ = [1 −j 1 j]^(T) W₁ ^({1}) W₁ ^({12})/{squareroot over (2)} W₁ ^({123})/{square root over (3)} W₁ ^({1234})/2 2 u₂ =[1 1 −1 1]^(T) W₂ ^({1}) W₂ ^({12})/{square root over (2)} W₂^({123})/{square root over (3)} W₂ ^({3214})/2 3 u₃ = [1 j 1 −j]^(T) W₃^({1}) W₃ ^({12})/{square root over (2)} W₃ ^({123})/{square root over(3)} W₃ ^({3214})/2 4 u₄ = [1 (−1 − j)/{square root over (2)} −j (1 −j)/{square root over (2)}]^(T) W₄ ^({1}) W₄ ^({14})/{square root over(2)} W₄ ^({124})/{square root over (3)} W₄ ^({1234})/2 5 u₅ = [1 (1 −j)/{square root over (2)} j (−1 − j)/{square root over (2)}]^(T) W₅^({1}) W₅ ^({14})/{square root over (2)} W₅ ^({124})/{square root over(3)} W₅ ^({1234})/2 6 u₆ = [1 (1 + j)/{square root over (2)} −j (−1 +j)/{square root over (2)}]^(T) W₆ ^({1}) W₆ ^({13})/{square root over(2)} W₆ ^({134})/{square root over (3)} W₆ ^({1324})/2 7 u₇ = [1 (−1 +j)/{square root over (2)} j (1 + j)/{square root over (2)}]^(T) W₇^({1}) W₇ ^({13})/{square root over (2)} W₇ ^({134})/{square root over(3)} W₇ ^({1324})/2 8 u₈ = [1 −1 1 1]^(T) W₈ ^({1}) W₈ ^({12})/{squareroot over (2)} W₈ ^({124})/{square root over (3)} W₈ ^({1234})/2 9 u₉ =[1 −j −1 −j]^(T) W₉ ^({1}) W₉ ^({14})/{square root over (2)} W₉^({134})/{square root over (3)} W₉ ^({1234})/2 10 u₁₀ = [1 1 1 −1]^(T)W₁₀ ^({1}) W₁₀ ^({13})/{square root over (2)} W₁₀ ^({123})/{square rootover (3)} W₁₀ ^({1324})/2 11 u₁₁ = [1 j −1 j]^(T) W₁₁ ^({1}) W₁₁^({13})/{square root over (2)} W₁₁ ^({134})/{square root over (3)} W₁₁^({1324})/2 12 u₁₂ = [1 −1 −1 1]^(T) W₁₂ ^({1}) W₁₂ ^({12})/{square rootover (2)} W₁₂ ^({123})/{square root over (3)} W₁₂ ^({1234})/2 13 u₁₃ =[1 −1 1 −1]^(T) W₁₃ ^({1}) W₁₃ ^({13})/{square root over (2)} W₁₃^({123})/{square root over (3)} W₁₃ ^({1324})/2 14 u₁₄ = [1 1 −1 −1]^(T)W₁₄ ^({1}) W₁₄ ^({13})/{square root over (2)} W₁₄ ^({123})/{square rootover (3)} W₁₄ ^({3214})/2 15 u₁₅ = [1 1 1 1]^(T) W₁₅ ^({1}) W₁₅^({12})/{square root over (2)} W₁₅ ^({123})/{square root over (3)} W₁₅^({1234})/2

where W_(n) ^({s}) represents a matrix formed by a column set {s} of amatrix W_(n)=I−2u_(n)u_(n) ^(H)/u_(n) ^(H)u_(n), and I is a 4×4 identitymatrix.

A seventh aspect provides a user equipment, where the user equipmentincludes: a determining module, configured to determine a rank used forindicating the number of transmission layers, further configured todetermine a first precoding matrix in a codebook set corresponding tothe rank, where precoding matrices included in the codebook set arerepresented by a first codebook index and a second codebook index, andfurther configured to determine a first precoding matrix indicator PMIand a second PMI used for indicating the first precoding matrix, wherethe first PMI and the first codebook index have a first correspondence,and the second PMI and the second codebook index have a secondcorrespondence; and a sending module, configured to send, to a basestation, the first PMI and the second PMI that are used for indicatingthe first precoding matrix and determined by the determining module,where the precoding matrices W included in the codebook set satisfy thefollowing equation:

W=W₁×W₂, where

${W_{1} = \begin{bmatrix}X_{n} & 0 \\0 & X_{n}\end{bmatrix}},{X_{n} = \begin{bmatrix}1 & 1 & 1 & 1 \\q_{1}^{n} & q_{1}^{n + 8} & q_{1}^{n + 16} & q_{1}^{n + 24}\end{bmatrix}},$q₁=e^(j2π/32), and n=0, 1, . . . , 15; and

the first codebook index corresponds to one value of n, and a valuerange of n is a set {0, 1, 2, 3, 4, 5, 6, 7}, {8, 9, 10, 11, 12, 13, 14,15}, {0, 2, 4, 6, 8, 10, 12, 14}, or {1, 3, 5, 7, 9, 11, 13, 15}.

With reference to the seventh aspect, in a first possible implementationmanner of the seventh aspect, when the rank determined by thedetermining module is 1, W₂ satisfies the following equation:

${W_{2} \in \left\{ {{\frac{1}{A}\begin{bmatrix}Y \\{{\alpha(i)}Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{j\;{\alpha(i)}Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{{- {\alpha(i)}}Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{{- j}\;{\alpha(i)}Y}\end{bmatrix}}} \right\}},$

where Yε{e₁,e₂,e₃,e₄}, α(i)=q₁ ^(2(i-1)); when Y is e₁, α(i) is α(1);when Y is e₂, α(i) is α(2); when Y is e₃, α(i) is α(3); when Y is e₄,α(i) is α(4); e_(i) represents a column vector with a dimension of 4×1,where an i^(th) element in e_(i) is 1, all other elements are 0, andiε{1, 2, 3, 4}; A is a constant.

With reference to the seventh aspect, in a second possibleimplementation manner of the seventh aspect, when the rank determined bythe determining module is 2, W₂ satisfies the following equation:

$\mspace{20mu}{W_{2} \in \left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}} \right\}}$(Y₁, Y₂) ∈ {(e₁, e₁), (e₂, e₂), (e₃, e₃), (e₄, e₄), (e₁, e₂), (e₂, e₃), (e₁, e₄), (e₂, e₄)};  or$W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & Y_{2}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{- Y_{1}} & Y_{2}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{- Y_{1}} & {- Y_{2}}\end{bmatrix}}} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ \left( {e_{2},e_{4}} \right) \right\}$$W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ {\left( {e_{1},e_{1}} \right),\left( {e_{2},e_{2}} \right),\left( {e_{3},e_{3}} \right),\left( {e_{4},e_{4}} \right)} \right\}$$W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{2} & {- Y_{1}}\end{bmatrix}},} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ {\left( {e_{1},e_{3}} \right),\left( {e_{2},e_{4}} \right),\left( {e_{3},e_{1}} \right),\left( {e_{4},e_{2}} \right)} \right\}$

where e_(i) represents a column vector with a dimension of 4×1, ani^(th) element in e_(i) is 1, all other elements are 0, and iε{1, 2, 3,4}; B is a constant.

With reference to the seventh aspect, in a third possible implementationmanner of the seventh aspect, a precoding matrix set corresponding tothe first codebook index corresponding to the first PMI includesprecoding matrices U1 and U2, where the precoding matrices U1 and U2 areindicated by the second codebook index, where:

${{U\; 1} = {\frac{1}{A}\begin{bmatrix}v \\{\beta\; v}\end{bmatrix}}},{{U\; 2} = {\frac{1}{A}\begin{bmatrix}v \\{{- \beta}\; v}\end{bmatrix}}},{v = \begin{bmatrix}1 \\q_{1}^{n + {({8n\mspace{14mu}{mod}\mspace{14mu} 32})}}\end{bmatrix}},$β=j^(└n/4┘)*α(i), i=(n mod 4)+1, α(i)=q₁ ^(2(i-1)), and A is a constant.

With reference to the first possible implementation manner of theseventh aspect, in a fourth possible implementation manner of theseventh aspect, when the rank determined by the determining module is 1,the precoding matrices W included in the codebook set are determinedaccording to Table A:

TABLE A i₂ i₁ 0 1 2 3 0-15 W_(i) ₁ _(,0) ⁽¹⁾ W_(i) ₁ _(,1) ⁽¹⁾ W_(i) ₁_(,2) ⁽¹⁾ W_(i) ₁ _(,3) ⁽¹⁾ i₂ i₁ 4 5 6 7 0-15 W_(i) ₁ _(+8,0) ⁽¹⁾ W_(i)₁ _(+8,1) ⁽¹⁾ W_(i) ₁ _(+8,2) ⁽¹⁾ W_(i) ₁ _(+8,3) ⁽¹⁾ i₂ i₁ 8 9 10 110-15 W_(i) ₁ _(+16,0) ⁽¹⁾ W_(i) ₁ _(+16,1) ⁽¹⁾ W_(i) ₁ _(+16,2) ⁽¹⁾W_(i) ₁ _(+16,3) ⁽¹⁾ i₂ i₁ 12 13 14 15 0-15 W_(i) ₁ _(+24,0) ⁽¹⁾ W_(i) ₁_(+24,1) ⁽¹⁾ W_(i) ₁ _(+24,2) ⁽¹⁾ W_(i) ₁ _(+24,3) ⁽¹⁾

where

${W_{m,k}^{(1)} = {\frac{1}{2}\begin{bmatrix}v_{m} \\{\varphi_{k}{\gamma(m)}v_{m}}\end{bmatrix}}},{{\gamma(m)} = e^{j\; 2\pi\frac{{({m - i_{1}})}/4}{32}}},{v_{m} = \begin{bmatrix}1 & e^{j\; 2\pi\;{m/32}}\end{bmatrix}},$φ_(k)=e^(jπk/2), and m and k are nonnegative integers; i₁ represents thefirst codebook index; i₂ represents the second codebook index.

With reference to the second possible implementation manner of theseventh aspect, in a fifth possible implementation manner of the seventhaspect, when the rank determined by the determining module is 2, theprecoding matrices W included in the codebook set are determinedaccording to Table B1 or B2:

TABLE B1 i₂ i₁ 0 1 2 3 0-15 W_(i) ₁ _(,i) ₁ _(,0) ⁽²⁾ W_(i) ₁ _(,i) ₁_(,1) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+8,0) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+8,1) ⁽²⁾ i₂i₁ 4 5 6 7 0-15 W_(i) ₁ _(+16,i) ₁ _(+16,0) ⁽²⁾ W_(i) ₁ _(+16,i) ₁_(+16,1) ⁽²⁾ W_(i) ₁ _(+24,i) ₁ _(+24,0) ⁽²⁾ W_(i) ₁ _(+24,i) ₁ _(+24,1)⁽²⁾ i₂ i₁ 8 9 10 11 0-15 W_(i) ₁ _(,i) ₁ _(+8,0) ⁽²⁾ W_(i) ₁ _(,i) ₁_(+8,1) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+16,0) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+16,1)⁽²⁾ i₂ i₁ 12 13 14 15 0-15 W_(i) ₁ _(,i) ₁ _(+24,0) ⁽²⁾ W_(i) ₁ _(,i) ₁_(+24,1) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+24,0) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+24,1)⁽²⁾

TABLE B2 i₂ i₁ 0 1 2 3 0-15 W_(i) ₁ _(,i) ₁ _(,0) ⁽²⁾ W_(i) ₁ _(,i) ₁_(,1) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+8,0) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+8,1) ⁽²⁾ i₂i₁ 4 5 6 7 0-15 W_(i) ₁ _(+16,i) ₁ _(+16,0) ⁽²⁾ W_(i) ₁ _(+16,i) ₁_(+16,1) ⁽²⁾ W_(i) ₁ _(+24,i) ₁ _(+24,0) ⁽²⁾ W_(i) ₁ _(+24,i) ₁ _(+24,1)⁽²⁾ i₂ i₁ 8 9 10 11 0-15 {tilde over (W)}_(i) ₁ _(+8,i) ₁ _(+24,0) ⁽²⁾W_(i) ₁ _(+8,i) ₁ _(+24,0) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+24,2) ⁽²⁾ {tildeover (W)}_(i) ₁ _(+8,i) ₁ _(+24,2) ⁽²⁾ i₂ i₁ 12 13 14 15 0-15

where

${W_{m,m^{\prime},k}^{(2)} = {\frac{1}{\sqrt{8}}\begin{bmatrix}v_{m} & v_{m^{\prime}} \\{\varphi_{k}v_{m}} & {{- \varphi_{k}}v_{m^{\prime}}}\end{bmatrix}}},{{\overset{\sim}{W}}_{m,m^{\prime},k}^{(2)} = {\frac{1}{\sqrt{8}}\begin{bmatrix}v_{m} & v_{m^{\prime}} \\{\varphi_{k}v_{m}} & {\varphi_{k}v_{m^{\prime}}}\end{bmatrix}}},{{\overset{\overset{\sim}{\sim}}{W}}_{m,m^{\prime},k}^{(2)} = {\frac{1}{\sqrt{8}}\begin{bmatrix}v_{m} & v_{m^{\prime}} \\{\varphi_{k}v_{m^{\prime}}} & {{- \varphi_{k}}v_{m}}\end{bmatrix}}},{v_{m} = \begin{bmatrix}1 & e^{j\; 2\pi\;{m/32}}\end{bmatrix}},{v_{m^{\prime}} = \begin{bmatrix}1 & e^{j\; 2\pi\;{m^{\prime}/32}}\end{bmatrix}},$φ_(k)=e^(jπk/2), and m, m′, and k are nonnegative integers; i₁represents the first codebook index; i₂ represents the second codebookindex.

With reference to the seventh aspect or any possible implementationmanner of the first to the fifth possible implementation manners of theseventh aspect, in a sixth possible implementation manner of the seventhaspect, when the rank determined by the determining module is 1, thefirst PMI, the second PMI, the first codebook index corresponding to thefirst PMI, and the second codebook index corresponding to the second PMIare determined according to Table C1, C2, C3, or C4:

TABLE C1 I_(PMI1) i₁ = I_(PMI1) I_(PMI2) i₂ 0 0 0 0 0 0 1 2 1 1 0 4 1 11 6 2 2 0 8 2 2 1 10 3 3 0 12 3 3 1 14 4 4 0 1 4 4 1 3 5 5 0 5 5 5 1 7 66 0 9 6 6 1 11 7 7 0 13 7 7 1 15

TABLE C2 I_(PMI1) i₁ = I_(PMI1) + 8 I_(PMI2) i₂ 0 8 0 0 0 8 1 2 1 9 0 41 9 1 6 2 10 0 8 2 10 1 10 3 11 0 12 3 11 1 14 4 12 0 1 4 12 1 3 5 13 05 5 13 1 7 6 14 0 9 6 14 1 11 7 15 0 13 7 15 1 15

TABLE C3 I_(PMI1) i₁ = 2I_(PMI1) I_(PMI2) i₂ 0 0 0 0 0 0 1 2 1 2 0 8 1 21 10 2 4 0 1 2 4 1 3 3 6 0 9 3 6 1 11 4 8 0 0 4 8 1 2 5 10 0 8 5 10 1 106 12 0 1 6 12 1 3 7 14 0 9 7 14 1 11

TABLE C4 I_(PMI1) i₁ = 2I_(PMI1) + 1 I_(PMI2) i₂ 0 1 0 4 0 1 1 6 1 3 012 1 3 1 14 2 5 0 5 2 5 1 7 3 7 0 13 3 7 1 15 4 9 0 4 4 9 1 6 5 11 0 125 11 1 14 6 13 0 5 6 13 1 7 7 15 0 13 7 15 1 15

where I_(PMI1) represents the first PMI, I_(PMI2) represents the secondPMI, i₁ represents the first codebook index, and i₂ represents thesecond codebook index.

With reference to the seventh aspect or any possible implementationmanner of the first to the fifth possible implementation manners of theseventh aspect, in a seventh possible implementation manner of theseventh aspect, when the rank determined by the determining module is 2,the value range of n may be the set {0, 1, 2, 3, 4, 5, 6, 7} or {8, 9,10, 11, 12, 13, 14, 15}.

An eighth aspect provides a user equipment, where the user equipmentincludes: a determining module, configured to determine a rank used forindicating the number of transmission layers, further configured todetermine a value of a first codebook index corresponding to oneprecoding matrix set in a codebook set, where the codebook setcorresponds to the rank, and precoding matrices included in the codebookset are represented by the first codebook index and a second codebookindex, and further configured to determine a jointly coded valuecorresponding to the rank and the value of the first codebook index,where the jointly coded value and the rank have a first correspondence,and the jointly coded value and the first codebook index have a secondcorrespondence; and a sending module, configured to send the jointlycoded value determined by the determining module to a base station,where the precoding matrices W included in the codebook set satisfy thefollowing equation:

W=W₁×W₂, where

${W_{1} = \begin{bmatrix}X_{n} & 0 \\0 & X_{n}\end{bmatrix}},{X_{n} = \begin{bmatrix}1 & 1 & 1 & 1 \\q_{1}^{n} & q_{1}^{n + 8} & q_{1}^{n + 16} & q_{1}^{n + 24}\end{bmatrix}},$q₁=e^(j2π/32), and n=0, 1, . . . , 15; and the first codebook indexcorresponds to one value of n, and a value range of n is a set {0, 1, 2,3, 4, 5, 6, 7}, {8, 9, 10, 11, 12, 13, 14, 15}, {0, 2, 4, 6}, {1, 3, 5,7}, {8, 10, 12, 14}, or {9, 11, 13, 15}.

With reference to the eighth aspect, in a first possible implementationmanner of the eighth aspect, when the rank determined by the determiningmodule is 1, W₂ satisfies the following equation:

${W_{2} \in \left\{ {{\frac{1}{A}\begin{bmatrix}Y \\{{\alpha(i)}Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{j\;{\alpha(i)}Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{{- {\alpha(i)}}Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{{- j}\;{\alpha(i)}Y}\end{bmatrix}}} \right\}},$

where Yε{e₁,e₂,e₃,e₄}, α(i)=q₁ ^(2(i-1)); when Y is e₁, α(i) is α(1);when Y is e₂, α(i) is α(2); when Y is e₃, α(i) is α(3); when Y is e₄,α(i) is α(4); e_(i) represents a column vector with a dimension of 4×1,where an i^(th) element in e_(i) is 1, all other elements are 0, andiε{1, 2, 3, 4}; A is a constant.

With reference to the eighth aspect, in a second possible implementationmanner of the eighth aspect, when the rank determined by the determiningmodule is 2, W₂ satisfies the following equation:

$\mspace{20mu}{W_{2} \in \left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}} \right\}}$(Y₁, Y₂) ∈ {(e₁, e₁), (e₂, e₂), (e₃, e₃), (e₄, e₄), (e₁, e₂), (e₂, e₃), (e₁, e₄), (e₂, e₄)};  or$W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & Y_{2}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{- Y_{1}} & Y_{2}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{- Y_{1}} & {- Y_{2}}\end{bmatrix}}} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ \left( {e_{2},e_{4}} \right) \right\}$$W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ {\left( {e_{1},e_{1}} \right),\left( {e_{2},e_{2}} \right),\left( {e_{3},e_{3}} \right),\left( {e_{4},e_{4}} \right)} \right\}$$W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{2} & {- Y_{1}}\end{bmatrix}},} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ {\left( {e_{1},e_{3}} \right),\left( {e_{2},e_{4}} \right),\left( {e_{3},e_{1}} \right),\left( {e_{4},e_{2}} \right)} \right\}$

where e_(i) represents a column vector with a dimension of 4×1, ani^(th) element in e_(i) is 1, all other elements are 0, and iε{1, 2, 3,4}; B is a constant.

With reference to the eighth aspect or either possible implementationmanner of the first to the second possible implementation manners of theeighth aspect, in a third possible implementation manner of the eighthaspect, when the number of bits bearing the jointly coded value is 4,the correspondence between the jointly coded value and the rank and thecorrespondence between the jointly coded value and the first codebookindex are determined according to the following Table D:

TABLE D I_(RI/PMI1) RI i₁ 0-7 1 I_(RI/PMI1)  8-15 2 I_(RI/PMI1) − 8where I_(RI/PMI1) represents the jointly coded value, RI represents therank, and represents the first codebook index.

With reference to the eighth aspect or either possible implementationmanner of the first to the second possible implementation manners of theeighth aspect, in a fourth possible implementation manner of the eighthaspect, when the number of bits bearing the jointly coded value is 3,the correspondence between the jointly coded value and the rank and thecorrespondence between the jointly coded value and the first codebookindex are determined according to the following Table E:

TABLE E I_(RI/PMI1) RI i₁ 0-3 1 2 × I_(RI/PMI1) 4-7 2 2 × (I_(RI/PMI1) −4)

where I_(R1/PMI1) represents the jointly coded value, RI represents therank, and represents the first codebook index.

A ninth aspect provides a user equipment, where the user equipmentincludes a determining module, configured to determine a rank used forindicating the number of transmission layers, further configured todetermine a first precoding matrix in a codebook set corresponding tothe rank, where precoding matrices included in the codebook set arerepresented by a first codebook index and a second codebook index, andfurther configured to determine a second precoding matrix indicator PMIused for indicating the first precoding matrix, where the second PMI andthe second codebook index have a first correspondence, and for one givenfirst codebook index, a value range of the second codebook indexcorresponding to a value range of the second PMI is a proper subset of avalue range of the second codebook index; and a sending module,configured to send, to a base station, the second PMI that is used forindicating the first precoding matrix and determined by the determiningmodule, where the precoding matrices W included in the codebook setsatisfy the following equation:

W=W₁×W₂, where

${W_{1} = \begin{bmatrix}X_{n} & 0 \\0 & X_{n}\end{bmatrix}},{X_{n} = \begin{bmatrix}1 & 1 & 1 & 1 \\q_{1}^{n} & q_{1}^{n + 8} & q_{1}^{n + 16} & q_{1}^{n + 24}\end{bmatrix}},$q₁=e^(j2π/32), and n=0, 1, . . . , 15;

the first codebook index corresponds to one value of n, and a valuerange of n is a set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14,15}; and

when the rank determined by the determining module is 2, in precodingmatrix sets that are determined according to the first codebook indexand the second codebook index corresponding to the value range of thesecond PMI, a first precoding matrix set corresponding to a firstcodebook index i_(1,a) and a second precoding matrix set correspondingto a first codebook index i_(1,a+8) are mutually exclusive, where thefirst codebook index i_(1,a) represents a first codebook indexcorresponding to n whose value is a, the first codebook index i_(1,a+8)represents a first codebook index corresponding to n whose value is a+8,and aε{0, 1, 2, 3, 4, 5, 6, 7}.

With reference to the ninth aspect, in a first possible implementationmanner of the ninth aspect, when the rank determined by the determiningmodule is 1, W₂ satisfies the following equation:

${W_{2} \in \left\{ {{\frac{1}{A}\begin{bmatrix}Y \\{{\alpha(i)}Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{j\;{\alpha(i)}Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{{- {\alpha(i)}}Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{{- j}\;{\alpha(i)}Y}\end{bmatrix}}} \right\}},$

where Yε{e₁,e₂,e₃,e₄}, α(i)=q₁ ^(2(i-1)); when Y is e₁, α(i) is α(1);when Y is e₂, α(i) is α(2); when Y is e₃, α(i) is α(3); when Y is e₄,α(i) is α(4); e_(i) represents a column vector with a dimension of 4×1,where an i^(th) element in e_(i) is 1, all other elements are 0, andiε{1, 2, 3, 4}; A is a constant.

With reference to the ninth aspect, in a second possible implementationmanner of the ninth aspect, when the rank determined by the determiningmodule is 2, W₂ satisfies the following equation:

${W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ {\left( {e_{1},e_{1}} \right),\left( {e_{2},e_{2}} \right),\left( {e_{3},e_{3}} \right),\left( {e_{4},e_{4}} \right),\left( {e_{1},e_{2}} \right),\left( {e_{2},e_{3}} \right),\left( {e_{1},e_{4}} \right),\left( {e_{2},e_{4}} \right)} \right\}};{or}$$W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & Y_{2}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{- Y_{1}} & Y_{2}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{- Y_{1}} & {- Y_{2}}\end{bmatrix}}} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ \left( {e_{2},e_{4}} \right) \right\}$$W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ {\left( {e_{1},e_{1}} \right),\left( {e_{2},e_{2}} \right),\left( {e_{3},e_{3}} \right),\left( {e_{4},e_{4}} \right)} \right\}$$W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{2} & {- Y_{1}}\end{bmatrix}},} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ {\left( {e_{1},e_{3}} \right),\left( {e_{2},e_{4}} \right),\left( {e_{3},e_{1}} \right),\left( {e_{4},e_{2}} \right)} \right\}$

where e_(i) represents a column vector with a dimension of 4×1, ani^(th) element in e_(i) is 1, all other elements are 0, and iε{1, 2, 3,4}; B is a constant.

With reference to the ninth aspect or either possible implementationmanner of the first to the second possible implementation manners of theninth aspect, in a third possible implementation manner of the ninthaspect, when the rank determined by the determining module is 2, mutualrelationships between the second PMI, the first codebook index, and thesecond codebook index are determined according to Table F1 or F2:

TABLE F1 I_(PMI2) i₁ i₂ 0-3 0-7 2 × I_(PMI2)  8-15 2 × I_(PMI2) + 1

TABLE F2 I_(PMI2) i₁ i₂ 0-3 0-7 2 × I_(PMI2)  8-15 2 × I_(PMI2) + 8

where I_(PMI2) represents the second PMI, i₁ represents the firstcodebook index, and i₂ represents the second codebook index.

With reference to the ninth aspect or either possible implementationmanner of the first to the second possible implementation manners of theninth aspect, in a fourth possible implementation manner of the ninthaspect, when the rank determined by the determining module is 3 or 4,the precoding matrices included in the codebook set corresponding to therank are:

four precoding matrices with codebook indexes 0 to 3 in Table G; or

four precoding matrices with codebook indexes 4 to 7 in Table G; or

four precoding matrices with codebook indexes 12 to 15 in Table G,

TABLE G Codebook RI Index u_(n) 1 2 3 4 0 u₀ = [1 −1 −1 −1]^(T) W₀^({1}) W₀ ^({14})/{square root over (2)} W₀ ^({124})/{square root over(3)} W₀ ^({1234})/2 1 u₁ = [1 −j 1 j]^(T) W₁ ^({1}) W₁ ^({12})/{squareroot over (2)} W₁ ^({123})/{square root over (3)} W₁ ^({1234})/2 2 u₂ =[1 1 −1 1]^(T) W₂ ^({1}) W₂ ^({12})/{square root over (2)} W₂^({123})/{square root over (3)} W₂ ^({3214})/2 3 u₃ = [1 j 1 −j]^(T) W₃^({1}) W₃ ^({12})/{square root over (2)} W₃ ^({123})/{square root over(3)} W₃ ^({3214})/2 4 u₄ = [1 (−1 − j)/{square root over (2)} −j (1 −j)/{square root over (2)}]^(T) W₄ ^({1}) W₄ ^({14})/{square root over(2)} W₄ ^({124})/{square root over (3)} W₄ ^({1234})/2 5 u₅ = [1 (1 −j)/{square root over (2)} j (−1 − j)/{square root over (2)}]^(T) W₅^({1}) W₅ ^({14})/{square root over (2)} W₅ ^({124})/{square root over(3)} W₅ ^({1234})/2 6 u₆ = [1 (1 + j)/{square root over (2)} −j (−1 +j)/{square root over (2)}]^(T) W₆ ^({1}) W₆ ^({13})/{square root over(2)} W₆ ^({134})/{square root over (3)} W₆ ^({1324})/2 7 u₇ = [1 (−1 +j)/{square root over (2)} j (1 + j)/{square root over (2)}]^(T) W₇^({1}) W₇ ^({13})/{square root over (2)} W₇ ^({134})/{square root over(3)} W₇ ^({1324})/2 8 u₈ = [1 −1 1 1]^(T) W₈ ^({1}) W₈ ^({12})/{squareroot over (2)} W₈ ^({124})/{square root over (3)} W₈ ^({1234})/2 9 u₉ =[1 −j −1 −j]^(T) W₉ ^({1}) W₉ ^({14})/{square root over (2)} W₉^({134})/{square root over (3)} W₉ ^({1234})/2 10 u₁₀ = [1 1 1 −1]^(T)W₁₀ ^({1}) W₁₀ ^({13})/{square root over (2)} W₁₀ ^({123})/{square rootover (3)} W₁₀ ^({1324})/2 11 u₁₁ = [1 j −1 j]^(T) W₁₁ ^({1}) W₁₁^({13})/{square root over (2)} W₁₁ ^({134})/{square root over (3)} W₁₁^({1324})/2 12 u₁₂ = [1 −1 −1 1]^(T) W₁₂ ^({1}) W₁₂ ^({12})/{square rootover (2)} W₁₂ ^({123})/{square root over (3)} W₁₂ ^({1234})/2 13 u₁₃ =[1 −1 1 −1]^(T) W₁₃ ^({1}) W₁₃ ^({13})/{square root over (2)} W₁₃^({123})/{square root over (3)} W₁₃ ^({1324})/2 14 u₁₄ = [1 1 −1 −1]^(T)W₁₄ ^({1}) W₁₄ ^({13})/{square root over (2)} W₁₄ ^({123})/{square rootover (3)} W₁₄ ^({3214})/2 15 u₁₅ = [1 1 1 1]^(T) W₁₅ ^({1}) W₁₅^({12})/{square root over (2)} W₁₅ ^({123})/{square root over (3)} W₁₅^({1234})/2

where W_(n) ^({s}) represents a matrix formed by a column set {s} of amatrix W_(n)=I−2u_(n)u_(n) ^(H)/u_(n) ^(H)u_(n), and I is a 4×4 identitymatrix.

A tenth aspect provides a base station, where the base station includesa receiving module, configured to receive a rank used for indicating thenumber of transmission layers, a first precoding matrix indicator PMI,and a second PMI that are sent by a user equipment; and a determiningmodule, configured to determine, according to the first PMI and thesecond PMI received by the receiving module, a first precoding matrix ina codebook set corresponding to the rank received by the receivingmodule, where precoding matrices included in the codebook set arerepresented by a first codebook index and a second codebook index, thefirst PMI and the first codebook index have a first correspondence, andthe second PMI and the second codebook index have a secondcorrespondence, where the precoding matrices W included in the codebookset satisfy the following equation:

W=W₁×W₂, where

${W_{1} = \begin{bmatrix}X_{n} & 0 \\0 & X_{n}\end{bmatrix}},{X_{n} = \begin{bmatrix}1 & 1 & 1 & 1 \\q_{1}^{n} & q_{1}^{n + 8} & q_{1}^{n + 16} & q_{1}^{n + 24}\end{bmatrix}},$q₁=e^(j2π/32), and n=0, 1, . . . , 15; and

the first codebook index corresponds to one value of n, and a valuerange of n is a set {0, 1, 2, 3, 4, 5, 6, 7}, {8, 9, 10, 11, 12, 13, 14,15}, {0, 2, 4, 6, 8, 10, 12, 14}, or {1, 3, 5, 7, 9, 11, 13, 15}.

With reference to the tenth aspect, in a first possible implementationmanner of the tenth aspect, when the rank received by the receivingmodule is 1, W₂ satisfies the following equation:

${W_{2} \in \left\{ {{\frac{1}{A}\begin{bmatrix}Y \\{{\alpha(i)}Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{j\;{\alpha(i)}Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{{- {\alpha(i)}}Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{{- j}\;{\alpha(i)}Y}\end{bmatrix}}} \right\}},$

where Yε{e₁,e₂,e₃,e₄}, α(i)=q₁ ^(2(i-1)); when Y is e₁, α(i) is α(1);when Y is e₂, α(i) is α(2); when Y is e₃, α(i) is α(3); when Y is e₄,α(i) is α(4); e_(i) represents a column vector with a dimension of 4×1,where an i^(th) element in e_(i) is 1, all other elements are 0, andiε{1, 2, 3, 4}; A is a constant.

With reference to the tenth aspect, in a second possible implementationmanner of the tenth aspect, when the rank received by the receivingmodule is 2, W₂ satisfies the following equation:

${W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ {\left( {e_{1},e_{1}} \right),\left( {e_{2},e_{2}} \right),\left( {e_{3},e_{3}} \right),\left( {e_{4},e_{4}} \right),\left( {e_{1},e_{2}} \right),\left( {e_{2},e_{3}} \right),\left( {e_{1},e_{4}} \right),\left( {e_{2},e_{4}} \right)} \right\}};{or}$$W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & Y_{2}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{- Y_{1}} & Y_{2}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{- Y_{1}} & {- Y_{2}}\end{bmatrix}}} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ \left( {e_{2},e_{4}} \right) \right\}$$W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ {\left( {e_{1},e_{1}} \right),\left( {e_{2},e_{2}} \right),\left( {e_{3},e_{3}} \right),\left( {e_{4},e_{4}} \right)} \right\}$$W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{2} & {- Y_{1}}\end{bmatrix}},} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ {\left( {e_{1},e_{3}} \right),\left( {e_{2},e_{4}} \right),\left( {e_{3},e_{1}} \right),\left( {e_{4},e_{2}} \right)} \right\}$

where e_(i) represents a column vector with a dimension of 4×1, ani^(th) element in e_(i) is 1, all other elements are 0, and iε{1, 2, 3,4}; B is a constant.

With reference to the tenth aspect, in a third possible implementationmanner of the tenth aspect, a precoding matrix set corresponding to thefirst codebook index corresponding to the first PMI includes precodingmatrices U1 and U2, where the precoding matrices U1 and U2 are indicatedby the second codebook index, where:

${{U\; 1} = {\frac{1}{A}\begin{bmatrix}v \\{\beta\; v}\end{bmatrix}}},{{U\; 2} = {\frac{1}{A}\begin{bmatrix}v \\{{- \beta}\; v}\end{bmatrix}}},{v = \begin{bmatrix}1 \\q_{1}^{n + {({8n\mspace{14mu}{mod}\mspace{14mu} 32})}}\end{bmatrix}},$β=j^(└n/4┘)*α(i), i=(n mod 4)+1, α(i)=q₁ ^(2(i-1)), and A is a constant.

With reference to the first possible implementation manner of the tenthaspect, in a fourth possible implementation manner of the tenth aspect,when the rank received by the receiving module is 1, the precodingmatrices W included in the codebook set are determined according toTable A:

TABLE A i₂ i₁ 0 1 2 3 0-15 W_(i) ₁ _(,0) ⁽¹⁾ W_(i) ₁ _(,1) ⁽¹⁾ W_(i) ₁_(,2) ⁽¹⁾ W_(i) ₁ _(,3) ⁽¹⁾ i₂ i₁ 4 5 6 7 0-15 W_(i) ₁ _(+8,0) ⁽¹⁾ W_(i)₁ _(+8,1) ⁽¹⁾ W_(i) ₁ _(+8,2) ⁽¹⁾ W_(i) ₁ _(+8,3) ⁽¹⁾ i₂ i₁ 8 9 10 110-15 W_(i) ₁ _(+16,0) ⁽¹⁾ W_(i) ₁ _(+16,1) ⁽¹⁾ W_(i) ₁ _(+16,2) ⁽¹⁾W_(i) ₁ _(+16,3) ⁽¹⁾ i₂ i₁ 12 13 14 15 0-15 W_(i) ₁ _(+24,0) ⁽¹⁾ W_(i) ₁_(+24,1) ⁽¹⁾ W_(i) ₁ _(+24,2) ⁽¹⁾ W_(i) ₁ _(+24,3) ⁽¹⁾

where

${W_{m,k}^{(1)} = {\frac{1}{2}\begin{bmatrix}v_{m} \\{\varphi_{k}{\gamma(m)}v_{m}}\end{bmatrix}}},{{\gamma(m)} = e^{j\; 2\pi\frac{{({m - i_{1}})}/4}{32}}},{v_{m} = \begin{bmatrix}1 & e^{j\; 2\pi\;{m/32}}\end{bmatrix}},$φ_(k)=e^(jπk/2), and m and k are nonnegative integers; i₁ represents thefirst codebook index; i₂ represents the second codebook index.

With reference to the second possible implementation manner of the tenthaspect, in a fifth possible implementation manner of the tenth aspect,when the rank received by the receiving module is 2, the precodingmatrices W included in the codebook set are determined according toTable B1 or B2:

TABLE B1 i₂ i₁ 0 1 2 3 0-15 W_(i) ₁ _(,i) ₁ _(,0) ⁽²⁾ W_(i) ₁ _(,i) ₁_(,1) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+8,0) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+8,1) ⁽²⁾ i₂i₁ 4 5 6 7 0-15 W_(i) ₁ _(+16,i) ₁ _(+16,0) ⁽²⁾ W_(i) ₁ _(+16,i) ₁_(+16,1) ⁽²⁾ W_(i) ₁ _(+24,i) ₁ _(+24,0) ⁽²⁾ W_(i) ₁ _(+24,i) ₁ _(+24,1)⁽²⁾ i₂ i₁ 8 9 10 11 0-15 W_(i) ₁ _(,i) ₁ _(+8,0) ⁽²⁾ W_(i) ₁ _(,i) ₁_(+8,1) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+16,0) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+16,1)⁽²⁾ i₂ i₁ 12 13 14 15 0-15 W_(i) ₁ _(,i) ₁ _(+24,0) ⁽²⁾ W_(i) ₁ _(,i) ₁_(+24,1) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+24,0) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+24,1)⁽²⁾

TABLE B2 i₂ i₁ 0 1 2 3 0-15 W_(i) ₁ _(,i) ₁ _(,0) ⁽²⁾ W_(i) ₁ _(,i) ₁_(,1) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+8,0) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+8,1) ⁽²⁾ i₂i₁ 4 5 6 7 0-15 W_(i) ₁ _(+16,i) ₁ _(+16,0) ⁽²⁾ W_(i) ₁ _(+16,i) ₁_(+16,1) ⁽²⁾ W_(i) ₁ _(+24,i) ₁ _(+24,0) ⁽²⁾ W_(i) ₁ _(+24,i) ₁ _(+24,1)⁽²⁾ i₂ i₁ 8 9 10 11 0-15 {tilde over (W)}_(i) ₁ _(+8,i) ₁ _(+24,0) ⁽²⁾W_(i) ₁ _(+8,i) ₁ _(+24,0) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+24,2) ⁽²⁾ {tildeover (W)}_(i) ₁ _(+8,i) ₁ _(+24,2) ⁽²⁾ i₂ i₁ 12 13 14 15 0-15

where

${W_{m,m^{\prime},k}^{(2)} = {\frac{1}{\sqrt{8}}\begin{bmatrix}v_{m} & v_{m^{\prime}} \\{\varphi_{k}v_{m}} & {{- \varphi_{k}}v_{m^{\prime}}}\end{bmatrix}}},{{\overset{\sim}{W}}_{m,m^{\prime},k}^{(2)} = {\frac{1}{\sqrt{8}}\begin{bmatrix}v_{m} & v_{m^{\prime}} \\{\varphi_{k}v_{m}} & {\varphi_{k}v_{m^{\prime}}}\end{bmatrix}}},{{\overset{\overset{\sim}{\sim}}{W}}_{m,m^{\prime},k}^{(2)} = {\frac{1}{\sqrt{8}}\begin{bmatrix}v_{m} & v_{m^{\prime}} \\{\varphi_{k}v_{m^{\prime}}} & {{- \varphi_{k}}v_{m}}\end{bmatrix}}},{v_{m} = \begin{bmatrix}1 & e^{j\; 2\pi\;{m/32}}\end{bmatrix}},{v_{m^{\prime}} = \begin{bmatrix}1 & e^{j\; 2\pi\;{m^{\prime}/32}}\end{bmatrix}},$φ_(k)=e^(jπk/2), and m, m′, and k are nonnegative integers; i₁represents the first codebook index; i₂ represents the second codebookindex.

With reference to the tenth aspect or any possible implementation mannerof the first to the fifth possible implementation manners of the tenthaspect, in a sixth possible implementation manner of the tenth aspect,when the rank received by the receiving module is 1, the first PMI, thesecond PMI, the first codebook index corresponding to the first PMI, andthe second codebook index corresponding to the second PMI are determinedaccording to Table C1, C2, C3, or C4:

TABLE C1 I_(PMI1) i₁ = I_(PMI1) I_(PMI2) i₂ 0 0 0 0 0 0 1 2 1 1 0 4 1 11 6 2 2 0 8 2 2 1 10 3 3 0 12 3 3 1 14 4 4 0 1 4 4 1 3 5 5 0 5 5 5 1 7 66 0 9 6 6 1 11 7 7 0 13 7 7 1 15

TABLE C2 I_(PMI1) i₁ = I_(PMI1) + 8 I_(PMI2) i₂ 0 8 0 0 0 8 1 2 1 9 0 41 9 1 6 2 10 0 8 2 10 1 10 3 11 0 12 3 11 1 14 4 12 0 1 4 12 1 3 5 13 05 5 13 1 7 6 14 0 9 6 14 1 11 7 15 0 13 7 15 1 15

TABLE C3 I_(PMI1) i₁ = 2I_(PMI1) I_(PMI2) i₂ 0 0 0 0 0 0 1 2 1 2 0 8 1 21 10 2 4 0 1 2 4 1 3 3 6 0 9 3 6 1 11 4 8 0 0 4 8 1 2 5 10 0 8 5 10 1 106 12 0 1 6 12 1 3 7 14 0 9 7 14 1 11

TABLE C4 I_(PMI1) i₁ = 2I_(PMI1) + 1 I_(PMI2) i₂ 0 1 0 4 0 1 1 6 1 3 012 1 3 1 14 2 5 0 5 2 5 1 7 3 7 0 13 3 7 1 15 4 9 0 4 4 9 1 6 5 11 0 125 11 1 14 6 13 0 5 6 13 1 7 7 15 0 13 7 15 1 15

where I_(PMI1) represents the first PMI, I_(PMI2) represents the secondPMI, i₁ represents the first codebook index, and i₂ represents thesecond codebook index.

With reference to the tenth aspect or any possible implementation mannerof the first to the fifth possible implementation manners of the tenthaspect, in a seventh possible implementation manner of the tenth aspect,when the rank received by the receiving module is 2, the value range ofn may be the set {0, 1, 2, 3, 4, 5, 6, 7} or {8, 9, 10, 11, 12, 13, 14,15}.

An eleventh aspect provides a base station, where the base stationincludes a receiving module, configured to receive a jointly coded valuesent by a user equipment; and a determining module, configured todetermine a value of a first codebook index and a rank used forindicating the number of transmission layers according to the jointlycoded value received by the receiving module, a correspondence betweenthe jointly coded value and the rank and a correspondence between thejointly coded value and the first codebook index, where the value of thefirst codebook index corresponds to one precoding matrix set in acodebook set, the codebook set corresponds to the rank, precodingmatrices included in the codebook set are represented by the firstcodebook index and a second codebook index, and the precoding matrices Wincluded in the codebook set satisfy the following equation:

W=W₁×W₂, where

${W_{1} = \begin{bmatrix}X_{n} & 0 \\0 & X_{n}\end{bmatrix}},{X_{n} = \begin{bmatrix}1 & 1 & 1 & 1 \\q_{1}^{n} & q_{1}^{n + 8} & q_{1}^{n + 16} & q_{1}^{n + 24}\end{bmatrix}},$q₁=e^(j2π/32), and n=0, 1, . . . , 15; and

the first codebook index corresponds to one value of n, and a valuerange of n is a set {0, 1, 2, 3, 4, 5, 6, 7}, {8, 9, 10, 11, 12, 13, 14,15}, {0, 2, 4, 6}, {1, 3, 5, 7}, {8, 10, 12, 14}, or {9, 11, 13, 15}.

With reference to the eleventh aspect, in a first possibleimplementation manner of the eleventh aspect, when the rank determinedby the determining module is 1, W₂ satisfies the following equation:

${W_{2} \in \left\{ {{\frac{1}{A}\begin{bmatrix}Y \\{{\alpha(i)}Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{j\;{\alpha(i)}Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{{- {\alpha(i)}}Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{{- j}\;{\alpha(i)}Y}\end{bmatrix}}} \right\}},$

where Yε{e₁,e₂,e₃,e₄}, α(i)=q₁ ^(2(i-1)); when Y is e₁, α(i) is α(1);when Y is e₁, α(i) is α(2); when Y is e₃, α(i) is α(3); when Y is e₄,α(i) is α(4); e_(i) represents a column vector with a dimension of 4×1,where an i^(th) element in e_(i) is 1, all other elements are 0, andiε{1, 2, 3, 4}; A is a constant.

With reference to the eleventh aspect, in a second possibleimplementation manner of the eleventh aspect, when the rank determinedby the determining module is 2, W₂ satisfies the following equation:

${W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ {\left( {e_{1},e_{1}} \right),\left( {e_{2},e_{2}} \right),\left( {e_{3},e_{3}} \right),\left( {e_{4},e_{4}} \right),\left( {e_{1},e_{2}} \right),\left( {e_{2},e_{3}} \right),\left( {e_{1},e_{4}} \right),\left( {e_{2},e_{4}} \right)} \right\}};{or}$$W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & Y_{2}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{- Y_{1}} & Y_{2}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{- Y_{1}} & {- Y_{2}}\end{bmatrix}}} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ \left( {e_{2},e_{4}} \right) \right\}$$W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ {\left( {e_{1},e_{1}} \right),\left( {e_{2},e_{2}} \right),\left( {e_{3},e_{3}} \right),\left( {e_{4},e_{4}} \right)} \right\}$$W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{2} & {- Y_{1}}\end{bmatrix}},} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ {\left( {e_{1},e_{3}} \right),\left( {e_{2},e_{4}} \right),\left( {e_{3},e_{1}} \right),\left( {e_{4},e_{2}} \right)} \right\}$

where e_(i) represents a column vector with a dimension of 4×1, ani^(th) element in e_(i) is 1, all other elements are 0, and iε{1, 2, 3,4}; B is a constant.

With reference to the eleventh aspect or either possible implementationmanner of the first to the second possible implementation manners of theeleventh aspect, in a third possible implementation manner of theeleventh aspect, when the number of bits bearing the jointly coded valueis 4, the correspondence between the jointly coded value and the rankand the correspondence between the jointly coded value and the firstcodebook index are determined according to the following Table D:

TABLE D I_(RI/PMI1) RI i₁ 0-7 1 I_(RI/PMI1)  8-15 2 I_(RI/PMI1) − 8

where I_(RI/PMI1) represents the jointly coded value, RI represents therank, and i₁ represents the first codebook index.

With reference to the eleventh aspect or either possible implementationmanner of the first to the second possible implementation manners of theeleventh aspect, in a fourth possible implementation manner of theeleventh aspect, when the number of bits bearing the jointly coded valueis 3, the correspondence between the jointly coded value and the rankand the correspondence between the jointly coded value and the firstcodebook index are determined according to the following Table E:

TABLE E I_(RI/PMI1) RI i₁ 0-3 1 2 × I_(RI/PMI1) 4-7 2 2 × (I_(RI/PMI1) −4)

where I_(RI/PMI1) represents the jointly coded value, RI represents therank, and i₁ represents the first codebook index.

A twelfth aspect provides a base station, where the base stationincludes a receiving module, configured to receive a second precodingmatrix indicator PMI, a first codebook index, and a rank used forindicating the number of transmission layers that are sent by a userequipment. The base station also includes a determining module,configured to determine, according to the second PMI and the firstcodebook index received by the receiving module, a first precodingmatrix in a codebook set corresponding to the rank received by thereceiving module, where precoding matrices included in the codebook setare represented by the first codebook index and a second codebook index,the second PMI and the second codebook index have a firstcorrespondence, and for one given first codebook index, a value range ofthe second codebook index corresponding to a value range of the secondPMI is a proper subset of a value range of the second codebook index,where the precoding matrices W included in the codebook set satisfy thefollowing equation:

W=W₁×W₂, where

${W_{1} = \begin{bmatrix}X_{n} & 0 \\0 & X_{n}\end{bmatrix}},{X_{n} = \begin{bmatrix}1 & 1 & 1 & 1 \\q_{1}^{n} & q_{1}^{n + 8} & q_{1}^{n + 16} & q_{1}^{n + 24}\end{bmatrix}},$q₁=e^(j2π/32), and n=0, 1, . . . , 15;

the first codebook index corresponds to one value of n, and a valuerange of n is a set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14,15}; and

when the received rank is 2, in precoding matrix sets that aredetermined according to the first codebook index and the second codebookindex corresponding to the value range of the second PMI, a firstprecoding matrix set corresponding to a first codebook index i_(1,a) anda second precoding matrix set corresponding to a first codebook indexi_(1,a+8) are mutually exclusive, where the first codebook index i_(1,a)represents a first codebook index corresponding to n whose value is a,the first codebook index i_(1,a+8) represents a first codebook indexcorresponding to n whose value is a+8, and aε{0, 1, 2, 3, 4, 5, 6, 7}.

With reference to the twelfth aspect, in a first possible implementationmanner of the twelfth aspect, when the rank received by the receivingmodule is 1, W₂ satisfies the following equation:

${W_{2} \in \left\{ {{\frac{1}{A}\begin{bmatrix}Y \\{{\alpha(i)}Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{j\;{\alpha(i)}Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{{- {\alpha(i)}}Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{{- j}\;{\alpha(i)}Y}\end{bmatrix}}} \right\}},$

where Yε{e₁,e₂,e₃,e₄}, α(i)=q₁ ^(2(i-1)); when Y is e₁, α(i) is α(1);when Y is e₂, α(i) is α(2); when Y is e₃, α(i) is α(3); when Y is e₄,α(i) is α(4); e_(i) represents a column vector with a dimension of 4×1,where an i^(th) element in e_(i) is 1, all other elements are 0, andiε{1, 2, 3, 4}; A is a constant.

With reference to the twelfth aspect, in a second possibleimplementation manner of the twelfth aspect, when the rank received bythe receiving module is 2, W₂ satisfies the following equation:

${W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ {\left( {e_{1},e_{1}} \right),\left( {e_{2},e_{2}} \right),\left( {e_{3},e_{3}} \right),\left( {e_{4},e_{4}} \right),\left( {e_{1},e_{2}} \right),\left( {e_{2},e_{3}} \right),\left( {e_{1},e_{4}} \right),\left( {e_{2},e_{4}} \right)} \right\}};{or}$$W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & Y_{2}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{- Y_{1}} & Y_{2}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{- Y_{1}} & {- Y_{2}}\end{bmatrix}}} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ \left( {e_{2},e_{4}} \right) \right\}$$W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ {\left( {e_{1},e_{1}} \right),\left( {e_{2},e_{2}} \right),\left( {e_{3},e_{3}} \right),\left( {e_{4},e_{4}} \right)} \right\}$$W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{2} & {- Y_{1}}\end{bmatrix}},} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ {\left( {e_{1},e_{3}} \right),\left( {e_{2},e_{4}} \right),\left( {e_{3},e_{1}} \right),\left( {e_{4},e_{2}} \right)} \right\}$

where e_(i) represents a column vector with a dimension of 4×1, ani^(th) element in e_(i) is 1, all other elements are 0, and iε{1, 2, 3,4}; B is a constant.

With reference to the twelfth aspect or either possible implementationmanner of the first to the second possible implementation manners of thetwelfth aspect, in a third possible implementation manner of the twelfthaspect, when the rank received by the receiving module is 2, mutualrelationships between the second PMI, the first codebook index, and thesecond codebook index are determined according to Table F1 or F2:

TABLE F1 I_(PMI2) i₁ i₂ 0-3 0-7 2 × I_(PMI2)  8-15 2 × I_(PMI2) + 1

TABLE F2 I_(PMI2) i₁ i₂ 0-3 0-7 2 × I_(PMI2)  8-15 2 × I_(PMI2) + 8

where I_(PMI2) represents the second PMI, i₁ represents the firstcodebook index, and i₂ represents the second codebook index.

With reference to the twelfth aspect or either possible implementationmanner of the first to the second possible implementation manners of thetwelfth aspect, in a fourth possible implementation manner of thetwelfth aspect, when the rank received by the receiving module is 3 or4, the precoding matrices included in the codebook set corresponding tothe rank are:

four precoding matrices with codebook indexes 0 to 3 in Table G; or

four precoding matrices with codebook indexes 4 to 7 in Table G; or

four precoding matrices with codebook indexes 12 to 15 in Table G,

TABLE G Codebook RI Index u_(n) 1 2 3 4 0 u₀ = [1 −1 −1 −1]^(T) W₀^({1}) W₀ ^({14})/{square root over (2)} W₀ ^({124})/{square root over(3)} W₀ ^({1234})/2 1 u₁ = [1 −j 1 j]^(T) W₁ ^({1}) W₁ ^({12})/{squareroot over (2)} W₁ ^({123})/{square root over (3)} W₁ ^({1234})/2 2 u₂ =[1 1 −1 1]^(T) W₂ ^({1}) W₂ ^({12})/{square root over (2)} W₂^({123})/{square root over (3)} W₂ ^({3214})/2 3 u₃ = [1 j 1 −j]^(T) W₃^({1}) W₃ ^({12})/{square root over (2)} W₃ ^({123})/{square root over(3)} W₃ ^({3214})/2 4 u₄ = [1 (−1 − j)/{square root over (2)} −j (1 −j)/{square root over (2)}]^(T) W₄ ^({1}) W₄ ^({14})/{square root over(2)} W₄ ^({124})/{square root over (3)} W₄ ^({1234})/2 5 u₅ = [1 (1 −j)/{square root over (2)} j (−1 − j)/{square root over (2)}]^(T) W₅^({1}) W₅ ^({14})/{square root over (2)} W₅ ^({124})/{square root over(3)} W₅ ^({1234})/2 6 u₆ = [1 (1 + j)/{square root over (2)} −j (−1 +j)/{square root over (2)}]^(T) W₆ ^({1}) W₆ ^({13})/{square root over(2)} W₆ ^({134})/{square root over (3)} W₆ ^({1324})/2 7 u₇ = [1 (−1 +j)/{square root over (2)} j (1 + j)/{square root over (2)}]^(T) W₇^({1}) W₇ ^({13})/{square root over (2)} W₇ ^({134})/{square root over(3)} W₇ ^({1324})/2 8 u₈ = [1 −1 1 1]^(T) W₈ ^({1}) W₈ ^({12})/{squareroot over (2)} W₈ ^({124})/{square root over (3)} W₈ ^({1234})/2 9 u₉ =[1 −j −1 −j]^(T) W₉ ^({1}) W₉ ^({14})/{square root over (2)} W₉^({134})/{square root over (3)} W₉ ^({1234})/2 10 u₁₀ = [1 1 1 −1]^(T)W₁₀ ^({1}) W₁₀ ^({13})/{square root over (2)} W₁₀ ^({123})/{square rootover (3)} W₁₀ ^({1324})/2 11 u₁₁ = [1 j −1 j]^(T) W₁₁ ^({1}) W₁₁^({13})/{square root over (2)} W₁₁ ^({134})/{square root over (3)} W₁₁^({1324})/2 12 u₁₂ = [1 −1 −1 1]^(T) W₁₂ ^({1}) W₁₂ ^({12})/{square rootover (2)} W₁₂ ^({123})/{square root over (3)} W₁₂ ^({1234})/2 13 u₁₃ =[1 −1 1 −1]^(T) W₁₃ ^({1}) W₁₃ ^({13})/{square root over (2)} W₁₃^({123})/{square root over (3)} W₁₃ ^({1324})/2 14 u₁₄ = [1 1 −1 −1]^(T)W₁₄ ^({1}) W₁₄ ^({13})/{square root over (2)} W₁₄ ^({123})/{square rootover (3)} W₁₄ ^({3214})/2 15 u₁₅ = [1 1 1 1]^(T) W₁₅ ^({1}) W₁₅^({12})/{square root over (2)} W₁₅ ^({123})/{square root over (3)} W₁₅^({1234})/2

where W_(n) ^({s}) represents a matrix formed by a column set {s} of amatrix W_(n)=I−2u_(n)u_(n) ^(H)/u_(n) ^(H)u_(n), and I is a 4×4 identitymatrix.

Based on the foregoing technical solutions, by means of the method fortransmitting a 4-antenna precoding matrix, and the user equipment andthe base station according to the embodiments of the present invention,more precoding matrices that are applicable to a uniform linear arrayantenna may be indicated without changing a feedback mode or feedbackbits, and it may be ensured that performance for application of adual-polarized antenna is not affected.

BRIEF DESCRIPTION OF THE DRAWINGS

To describe the technical solutions in the embodiments of the presentinvention more clearly, the following briefly introduces theaccompanying drawings required for describing the embodiments of thepresent invention. Apparently, the accompanying drawings in thefollowing description show merely some embodiments of the presentinvention, and a person of ordinary skill in the art may still deriveother drawings from these accompanying drawings without creativeefforts.

FIG. 1 is a schematic flowchart of a method for transmitting a 4-antennaprecoding matrix according to an embodiment;

FIG. 2 is another schematic flowchart of a method for transmitting a4-antenna precoding matrix according to an embodiment;

FIG. 3 is still another schematic flowchart of a method for transmittinga 4-antenna precoding matrix according to an embodiment;

FIG. 4 is a schematic flowchart of a method for transmitting a 4-antennaprecoding matrix according to another embodiment;

FIG. 5 is another schematic flowchart of a method for transmitting a4-antenna precoding matrix according to another embodiment;

FIG. 6 is still another schematic flowchart of a method for transmittinga 4-antenna precoding matrix according to another embodiment;

FIG. 7 is a schematic block diagram of a user equipment according to anembodiment;

FIG. 8 is another schematic block diagram of a user equipment accordingto an embodiment;

FIG. 9 is still another schematic block diagram of a user equipmentaccording to an embodiment;

FIG. 10 is a schematic block diagram of a base station according to anembodiment;

FIG. 11 is another schematic block diagram of a base station accordingto an embodiment;

FIG. 12 is still another schematic block diagram of a base stationaccording to an embodiment;

FIG. 13 is a schematic block diagram of a user equipment according toanother embodiment;

FIG. 14 is another schematic block diagram of a user equipment accordingto another embodiment;

FIG. 15 is still another schematic block diagram of a user equipmentaccording to another embodiment;

FIG. 16 is a schematic block diagram of a base station according toanother embodiment;

FIG. 17 is another schematic block diagram of a base station accordingto another embodiment; and

FIG. 18 is still another schematic block diagram of a base stationaccording to another embodiment.

DETAILED DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS

The following clearly describes the technical solutions in theembodiments of the present invention with reference to the accompanyingdrawings in the embodiments of the present invention. Apparently, thedescribed embodiments are a part rather than all of the embodiments ofthe present invention. All other embodiments obtained by a person ofordinary skill in the art based on the embodiments of the presentinvention without creative efforts shall fall within the protectionscope of the present invention.

It should be understood that, the technical solutions of the embodimentsmay be applied to various communications systems, such as: a GlobalSystem of Mobile Communications (“GSM” for short) system, a CodeDivision Multiple Access (“CDMA” for short) system, a Wideband CodeDivision Multiple Access (“WCDMA” for short) system, a general packetradio service (“GPRS” for short) system, a Long Term Evolution (“LTE”for short) system, an LTE frequency division duplex (“FDD” for short)system, an LTE time division duplex (“TDD” for short) system, aUniversal Mobile Telecommunications System (“UMTS” for short), aWorldwide Interoperability for Microwave Access (“WiMAX” for short)communications system or the like.

It should also be understood that in the embodiments of the presentinvention, a user equipment (“UE” for short) may be referred to as aterminal, a mobile station (“MS” for short), a mobile terminal, and thelike. The user equipment may communicate with one or more core networksthrough a radio access network (“RAN” for short). For example, the userequipment may be a mobile phone (also referred to as a “cellular” phone)or a computer with a mobile terminal. For example, the user equipmentmay also be a portable, pocket-sized, handheld, computer built-in, orvehicle-mounted mobile apparatus, which exchanges voice and/or data withthe radio access network.

In the embodiments of the present invention, a base station may be abase station (“BTS” for short) in GSM or CDMA, or may be a NodeB (“NB”for short) in WCDMA, or may be an evolved NodeB (“eNB” or “e-NodeB” forshort) in LTE, which is not limited in the present invention. However,for ease of description, the following embodiments are described byusing an eNB as an example.

FIG. 1 shows a schematic flowchart of a method 10 for transmitting a4-antenna precoding matrix according to an embodiment. The method 10 maybe performed, for example, by a user equipment. As shown in FIG. 1, themethod 10 includes the following steps.

S11. Determine a rank used for indicating the number of transmissionlayers.

S12. Determine a first precoding matrix in a codebook set correspondingto the rank, where precoding matrices included in the codebook set arerepresented by a first codebook index and a second codebook index.

S13. Determine a first precoding matrix indicator PMI and a second PMIused for indicating the first precoding matrix, where the first PMI andthe first codebook index have a first correspondence, and the second PMIand the second codebook index have a second correspondence.

S14. Send the first PMI and the second PMI used for indicating the firstprecoding matrix to a base station.

The precoding matrices W included in the codebook set satisfy thefollowing equation:

W=W₁×W₂, where

${W_{1} = \begin{bmatrix}X_{n} & 0 \\0 & X_{n}\end{bmatrix}},{X_{n} = \begin{bmatrix}1 & 1 & 1 & 1 \\q_{1}^{n} & q_{1}^{n + 8} & q_{1}^{n + 16} & q_{1}^{n + 24}\end{bmatrix}},$q₁=e^(j2π/32), and n=0, 1, . . . , 15; and

the first codebook index corresponds to one value of n, and a valuerange of n is a set {0, 1, 2, 3, 4, 5, 6, 7}, {8, 9, 10, 11, 12, 13, 14,15}, {0, 2, 4, 6, 8, 10, 12, 14}, or {1, 3, 5, 7, 9, 11, 13, 15}.

Therefore, by means of the method for transmitting a 4-antenna precodingmatrix according to this embodiment, more precoding matrices that areapplicable to a uniform linear array antenna may be indicated withoutchanging a feedback mode or feedback bits, and it may also be ensuredthat performance for application of a dual-polarized antenna is notaffected, so that system performance may be improved and user experiencemay be enhanced.

Specifically, in S11, the user equipment may determine the rank used forindicating the number of transmission layers, for example, based onchannel state information (“CSI” for short). It should be understoodthat the UE may determine the rank by using a method that is well knownto a person skilled in the art, which is not described herein anyfurther for brevity.

In S12, the user equipment UE may determine, in the codebook setcorresponding to the rank, for example, based on CSI, the firstprecoding matrix that the UE wants the eNB to use when the eNB sendsdownlink data. All precoding matrices included in the codebook setcorresponding to the rank may be represented, for example, by the firstcodebook index i₁ and the second codebook index i₂.

In this embodiment of the present invention, optionally, a value rangeof the first codebook index i₁ is 0≦i₁≦15, and a value range of thesecond codebook index i₂ is 0≦i₂≦L₂−1, where L₂ is a positive integer.For example, a value range of L₂ is 1≦L₂≦16, that is, the value range ofthe second codebook index i₂ is, for example, 0≦i₂≦15.

In S13, the UE may determine the first PMI and the second PMI used forindicating the first precoding matrix. That is, in this embodiment, allthe precoding matrices included in the codebook set corresponding to therank may be represented not only by the first codebook index i₁ and thesecond codebook index i₂, but also by the first PMI I_(PMI1) and thesecond PMI I_(PMI2).

In this embodiment, the first PMI I_(PMI1) and the first codebook indexi₁ may have the first correspondence, where the first correspondence maybe a functional relationship or a mapping relationship, for example,i₁=1*I_(PMI1). The second PMI I_(PMI1) and the second codebook index i₂may have the second correspondence, where the second correspondence maybe a functional relationship or a mapping relationship, for example, thesecond PMI I_(PMI2) is used for indicating a sequence number of a valuein the value range of the second codebook index i₂.

It should be understood that in this embodiment, a set formed byprecoding matrices represented by the first PMI I_(PMI1) and the secondPMI I_(PMI2) is a proper subset of the codebook set; that is, in thisembodiment of the present invention, the transmitted 4-antenna precodingmatrix is a 4-antenna precoding matrix on which subsampling(subsampling) is performed.

In S14, the user equipment sends the first PMI and the second PMI usedfor indicating the first precoding matrix to the base station on achannel, for example, a PUCCH channel, a physical uplink shared channel(“PUSCH” for short), or another channel.

Optionally, in this embodiment of the present invention, the userequipment sends the first PMI and the second PMI used for indicating thefirst precoding matrix to the base station on one uplink channel. Theuplink channel may be a channel such as a PUCCH or a PUSCH. For example,the user equipment transmits the first PMI and the second PMI used forindicating the first precoding matrix on one PUCCH, or the userequipment transmits the first PMI and the second PMI used for indicatingthe first precoding matrix on one PUSCH. It should be understood thatthe user equipment may also separately send the first PMI and the secondPMI used for indicating the first precoding matrix to the base station,and this embodiment of the present invention is not limited thereto.

In this embodiment of the present invention, the precoding matrices Wincluded in the codebook set corresponding to the rank satisfy thefollowing equation (4):W=W ₁ ×W ₂  (4)

where

${W_{1} = \begin{bmatrix}X_{n} & 0 \\0 & X_{n}\end{bmatrix}},{X_{n} = \begin{bmatrix}1 & 1 & 1 & 1 \\q_{1}^{n} & q_{1}^{n + 8} & q_{1}^{n + 16} & q_{1}^{n + 24}\end{bmatrix}},$q₁=e^(j2π/32), , and n=0, 1, . . . , 15.

In this embodiment, one first codebook index corresponds to one value ofn, and a value range of n is a set {0, 1, 2, 3, 4, 5, 6, 7}, {8, 9, 10,11, 12, 13, 14, 15}, {0, 2, 4, 6, 8, 10, 12, 14}, or {1, 3, 5, 7, 9, 11,13, 15}.

Optionally, in this embodiment, the first codebook index and n have thesame value. For example, when a value of the first codebook index is 1,a value of n is also 1; that is, when i₁=1, n=1. It should be understoodthat this embodiment is described merely by using a case that the firstcodebook index and n have the same value as an example, but the presentinvention is not limited thereto as long as the value of n is uniquelydetermined according to the value of the first codebook index.

In this embodiment, optionally, when the rank is determined to be 2, thevalue range of n may be the set {0, 1, 2, 3, 4, 5, 6, 7} or {8, 9, 10,11, 12, 13, 14, 15}.

In this embodiment of the present invention, optionally, when the rankis determined to be 1, W₂ satisfies the following equation (5):

$\begin{matrix}{{W_{2} \in \left\{ {{\frac{1}{A}\begin{bmatrix}Y \\{{\alpha(i)}Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{j\;{\alpha(i)}Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{{- {\alpha(i)}}Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{{- j}\;{\alpha(i)}Y}\end{bmatrix}}} \right\}},} & (5)\end{matrix}$

where Yε{e₁,e₂,e₃,e₄}, α(i)=q₁ ^(2(i-1)); when Y is e₁, α(i) is α(1);when Y is e₂, α(i) is α(2); when Y is e₃, α(i) is α(3); when Y is e₄,α(i) is α(4); e_(i) represents a column vector with a dimension of 4×1,where an i^(th) element in e_(i) is 1, all other elements are 0, andiε{1, 2, 3, 4}; A is a constant.

In this embodiment, optionally, when the rank is determined to be 1, theprecoding matrices W included in the codebook set are determinedaccording to Table A:

TABLE A i₂ i₁ 0 1 2 3 0-15 W_(i) ₁ _(,0) ⁽¹⁾ W_(i) ₁ _(,1) ⁽¹⁾ W_(i) ₁_(,2) ⁽¹⁾ W_(i) ₁ _(,3) ⁽¹⁾ i₂ i₁ 4 5 6 7 0-15 W_(i) ₁ _(+8,0) ⁽¹⁾ W_(i)₁ _(+8,1) ⁽¹⁾ W_(i) ₁ _(+8,2) ⁽¹⁾ W_(i) ₁ _(+8,3) ⁽¹⁾ i₂ i₁ 8 9 10 110-15 W_(i) ₁ _(+16,0) ⁽¹⁾ W_(i) ₁ _(+16,1) ⁽¹⁾ W_(i) ₁ _(+16,2) ⁽¹⁾W_(i) ₁ _(+16,3) ⁽¹⁾ i₂ i₁ 12 13 14 15 0-15 W_(i) ₁ _(+24,0) ⁽¹⁾ W_(i) ₁_(+24,1) ⁽¹⁾ W_(i) ₁ _(+24,2) ⁽¹⁾ W_(i) ₁ _(+24,3) ⁽¹⁾

where

${W_{m,k}^{(1)} = {\frac{1}{2}\begin{bmatrix}v_{m} \\{\varphi_{k}{\gamma(m)}v_{m}}\end{bmatrix}}},{{\gamma(m)} = e^{j\; 2\pi\frac{{({m - i_{1}})}/4}{32}}},{v_{m} = \begin{bmatrix}1 & e^{j\; 2\pi\;{m/32}}\end{bmatrix}},$φ_(k)=e^(jπk/2), and m and k are nonnegative integers; i₁ represents thefirst codebook index; i₂ represents the second codebook index.

In this embodiment, optionally, when the rank determined by the UE is 2,W₂ satisfies the following equation (6):

$\begin{matrix}{W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ {\left( {e_{1},e_{1}} \right),\left( {e_{2},e_{2}} \right),\left( {e_{3},e_{3}} \right),\left( {e_{4},e_{4}} \right),\left( {e_{1},e_{2}} \right),\left( {e_{2},e_{3}} \right),\left( {e_{1},e_{4}} \right),\left( {e_{2},e_{4}} \right)} \right\}} & (6)\end{matrix}$

where e_(i) represents a column vector with a dimension of 4×1, ani^(th) element in e_(i) is 1, all other elements are 0, and iε{1, 2, 3,4}; B is a constant.

In this embodiment, optionally, when the rank is determined to be 2, W₂satisfies the following equation (7):

$\begin{matrix}{{W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & Y_{2}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{- Y_{1}} & Y_{2}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{- Y_{1}} & {- Y_{2}}\end{bmatrix}}} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ \left( {e_{2},e_{4}} \right) \right\}}{W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ {\left( {e_{1},e_{1}} \right),\left( {e_{2},e_{2}} \right),\left( {e_{3},e_{3}} \right),\left( {e_{4},e_{4}} \right)} \right\}}{W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{2} & {- Y_{1}}\end{bmatrix}},} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ {\left( {e_{1},e_{3}} \right),\left( {e_{2},e_{4}} \right),\left( {e_{3},e_{1}} \right),\left( {e_{4},e_{2}} \right)} \right\}}} & (7)\end{matrix}$

where e_(i) represents a column vector with a dimension of 4×1, ani^(th) element in e_(i) is 1, all other elements are 0, and iε{1, 2, 3,4}; B is a constant.

That is, in this embodiment, when the user equipment determines that therank used for indicating the number of transmission layers is 2, W₂satisfies the equation (6) or W₂ satisfies the equation (7).

In this embodiment, optionally, when the rank determined by the UE is 2,the precoding matrices W included in the codebook set are determinedaccording to Table B1 or B2:

TABLE B1 i₂ i₁ 0 1 2 3 0-15 W_(i) ₁ _(,i) ₁ _(,0) ⁽²⁾ W_(i) ₁ _(,i) ₁_(,1) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+8,0) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+8,1) ⁽²⁾ i₂i₁ 4 5 6 7 0-15 W_(i) ₁ _(+16,i) ₁ _(+16,0) ⁽²⁾ W_(i) ₁ _(+16,i) ₁_(+16,1) ⁽²⁾ W_(i) ₁ _(+24,i) ₁ _(+24,0) ⁽²⁾ W_(i) ₁ _(+24,i) ₁ _(+24,1)⁽²⁾ i₂ i₁ 8 9 10 11 0-15 W_(i) ₁ _(,i) ₁ _(+8,0) ⁽²⁾ W_(i) ₁ _(,i) ₁_(+8,1) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+16,0) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+16,1)⁽²⁾ i₂ i₁ 12 13 14 15 0-15 W_(i) ₁ _(,i) ₁ _(+24,0) ⁽²⁾ W_(i) ₁ _(,i) ₁_(+24,1) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+24,0) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+24,1)⁽²⁾

TABLE B2 i₂ i₁ 0 1 2 3 0-15 W_(i) ₁ _(,i) ₁ _(,0) ⁽²⁾ W_(i) ₁ _(,i) ₁_(,1) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+8,0) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+8,1) ⁽²⁾ i₂i₁ 4 5 6 7 0-15 W_(i) ₁ _(+16,i) ₁ _(+16,0) ⁽²⁾ W_(i) ₁ _(+16,i) ₁_(+16,1) ⁽²⁾ W_(i) ₁ _(+24,i) ₁ _(+24,0) ⁽²⁾ W_(i) ₁ _(+24,i) ₁ _(+24,1)⁽²⁾ i₂ i₁ 8 9 10 11 0-15 {tilde over (W)}_(i) ₁ _(+8,i) ₁ _(+24,0) ⁽²⁾W_(i) ₁ _(+8,i) ₁ _(+24,0) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+24,2) ⁽²⁾ {tildeover (W)}_(i) ₁ _(+8,i) ₁ _(+24,2) ⁽²⁾ i₂ i₁ 12 13 14 15 0-15

where

${W_{m,m^{\prime},k}^{(2)} = {\frac{1}{\sqrt{8}}\begin{bmatrix}v_{m} & v_{m^{\prime}} \\{\varphi_{k}v_{m}} & {{- \varphi_{k}}v_{m^{\prime}}}\end{bmatrix}}},{{\overset{\sim}{W}}_{m,m^{\prime},k}^{(2)} = {\frac{1}{\sqrt{8}}\begin{bmatrix}v_{m} & v_{m^{\prime}} \\{\varphi_{k}v_{m}} & {\varphi_{k}v_{m^{\prime}}}\end{bmatrix}}},{{\overset{\overset{\sim}{\sim}}{W}}_{m,m^{\prime},k}^{(2)} = {\frac{1}{\sqrt{8}}\begin{bmatrix}v_{m} & v_{m^{\prime}} \\{\varphi_{k}v_{m^{\prime}}} & {{- \varphi_{k}}v_{m}}\end{bmatrix}}},{v_{m} = \begin{bmatrix}1 & e^{j\; 2\pi\;{m/32}}\end{bmatrix}},{v_{m^{\prime}} = \begin{bmatrix}1 & e^{j\; 2\pi\;{m^{\prime}/32}}\end{bmatrix}},$φ_(k)=e^(jπk/2), and m, m′, and k are nonnegative integers; i₁represents the first codebook index; i₂ represents the second codebookindex.

It should be understood that in the embodiments, Table A, Table B1, andTable B2 provide only one presentation manner of the precoding matrix W,where i₁ may correspond to W₁ in the precoding matrix W=W₁×W₂, and i₂may correspond to W₂. This embodiment is described merely by using thefirst codebook index, the second codebook index, and values thereof inTable A, Table B1, and Table B2 as an example, but the present inventionis not limited thereto. The precoding matrix W determined in Table A,Table B1, and Table B2 may be further represented by using another indexor another index value.

In this embodiment of the present invention, optionally, a precodingmatrix set corresponding to the first codebook index corresponding tothe first PMI includes precoding matrices U1 and U2, where the precodingmatrices U1 and U2 are indicated by the second codebook index, where:

${{U\; 1} = {\frac{1}{A}\begin{bmatrix}v \\{\beta\; v}\end{bmatrix}}},{{U\; 2} = {\frac{1}{A}\begin{bmatrix}v \\{{- \beta}\; v}\end{bmatrix}}},{v = \begin{bmatrix}1 \\q_{1}^{n + {({8n\mspace{14mu}{mod}\mspace{14mu} 32})}}\end{bmatrix}},$β=j^(└n/4┘)*α(i), i=(n mod 4)+1, α(i)=q₁ ^(2(i-1)), and A is a constant.

It should be understood that in this embodiment, “mod” represents amodulo operation.

Therefore, by means of the method for transmitting a 4-antenna precodingmatrix according to this embodiment, more precoding matrices that areapplicable to a uniform linear array antenna may be indicated withoutchanging a feedback mode or feedback bits, and it may also be ensuredthat performance for application of a dual-polarized antenna is notaffected, so that system performance may be improved and user experiencemay be enhanced.

In this embodiment, by analyzing a 4-antenna precoding matrix that isproposed in 3GPP and whose rank is i₁ it is known that a total of 16 DFTvectors are included in all 4-antenna precoding matrices/vectors whoserank is i₁ as shown in FIG. 7.

TABLE 7 i₁ i₂ DFT Vector 0  0 (select the first vector of W₁) Yes 1  6(select the second vector of W₁) Yes 2  8 (select the third vector ofW₁) Yes 3 14 (select the fourth vector of W₁) Yes 4  1 (select the firstvector of W₁) Yes 5  7 (select the second vector of W₁) Yes 6  9 (selectthe third vector of W₁) Yes 7 15 (select the fourth vector of W₁) Yes 8 2 (select the first vector of W₁) Yes 9  4 (select the second vector ofW₁) Yes 10 10 (select the third vector of W₁) Yes 11 12 (select thefourth vector of W₁) Yes 12  3 (select the first vector of W₁) Yes 13  5(select the second vector of W₁) Yes 14 11 (select the third vector ofW₁) Yes 15 13 (select the fourth vector of W₁) Yes

According to Table 7, when the value of the first codebook index i₁ or nis given, that is, W₁ is given, a DFT vector can be formed in only oneof four beam directions or four vectors. Moreover, for i₁ and i₁+8,where i₁=0, 1, 2, 3, 4, 5, 6, 7, X_(n) in W₁ includes four beamdirections which are the same, and a difference between them lies inthat a value of α(i) is different for a same beam direction.

For example, with respect to i₁=0,

${X_{0} = \begin{bmatrix}1 & 1 & 1 & 1 \\e^{j\; 2{{\pi{(0)}}/32}} & e^{j\; 2{{\pi{(8)}}/32}} & e^{j\; 2{{\pi{(16)}}/32}} & e^{j\; 2{{\pi{(24)}}/32}}\end{bmatrix}};$with respect to i₁=8,

$X_{8} = {\begin{bmatrix}1 & 1 & 1 & 1 \\e^{j\; 2{{\pi{(8)}}/32}} & e^{j\; 2{{\pi{(16)}}/32}} & e^{j\; 2{{\pi{(24)}}/32}} & e^{j\; 2{{\pi{(0)}}/32}}\end{bmatrix}.}$That is, when i₁=0, a first vector of X₀ is

$\begin{bmatrix}1 \\e^{j\; 2{{\pi{(0)}}/32}}\end{bmatrix};$when i₁=8, a first vector of X₈ is

$\begin{bmatrix}1 \\e^{j\; 2{{\pi{(8)}}/32}}\end{bmatrix}.$Therefore, a column shift is performed on the two of X₀ and X₈, butvectors included in X₀ and X₈ are the same.

In this embodiment, optionally, a value range of the first codebookindex corresponding to the first PMI and a value range of the secondcodebook index corresponding to the second PMI have an associationrelationship. Optionally, that a value range of the first codebook indexcorresponding to the first PMI and a value range of the second codebookindex corresponding to the second PMI have an association relationshipincludes the value range of the second codebook index corresponding tothe second PMI is uniquely determined according to the value and/or thevalue range of the first codebook index corresponding to the first PMI.

In this embodiment, optionally, that a value range of the first codebookindex corresponding to the first PMI and a value range of the secondcodebook index corresponding to the second PMI have an associationrelationship includes the value range of the first codebook indexcorresponding to the first PMI includes at least two first value setshaving different elements, the value range of the second codebook indexcorresponding to the second PMI includes at least two second value setshaving different elements, and the at least two first value sets and theat least two second value sets having a one-to-one correspondence.

It should be understood that the number of the first value sets is equalto the number of the second value sets. It should be further understoodthat the elements in the first value sets are different from each other,and the elements in the second value sets are also different from eachother.

Optionally, each first value set of the at least two first value setsincludes at least two values, and each second value set of the at leasttwo second value sets includes at least two values.

In this embodiment, the value range of the first codebook indexcorresponding to the first PMI and the value range of the secondcodebook index corresponding to the second PMI have an associationrelationship; therefore, by means of the method for transmitting aprecoding matrix according to this embodiment, more precoding matricesthat are applicable to a uniform linear array antenna may be indicatedwithout changing a feedback mode or feedback bits, and it may also beensured that performance for application of a dual-polarized antenna isnot affected, so that system performance may be improved and userexperience may be enhanced.

The following description uses mutual relationships between the firstPMI, the second PMI, the first codebook index corresponding to the firstPMI, and the second codebook index corresponding to the second PMI as anexample.

In this embodiment, optionally, when the rank is determined to be 1, thefirst PMI, the second PMI, the first codebook index corresponding to thefirst PMI, and the second codebook index corresponding to the second PMIare determined according to Table C1:

TABLE C1 I_(PMI1) i₁ = I_(PMI1) I_(PMI2) i₂ 0 0 0 0 0 0 1 2 1 1 0 4 1 11 6 2 2 0 8 2 2 1 10 3 3 0 12 3 3 1 14 4 4 0 1 4 4 1 3 5 5 0 5 5 5 1 7 66 0 9 6 6 1 11 7 7 0 13 7 7 1 15where I_(PMI1) represents the first PMI, I_(PMI2) represents the secondPMI, i₁ represents the first codebook index, and i₂ represents thesecond codebook index.

With reference to Table 7, it may be known that, when the first PMI, thesecond PMI, the first codebook index corresponding to the first PMI, andthe second codebook index corresponding to the second PMI have themutual relationships shown in Table C1, a codebook including 16precoding matrices on which subsampling is performed has a total of 8DFT vectors; in this case, as shown in Table C1, corresponding values ofthe second codebook index i₂ are 0, 1, 6, 7, 8, 9, 14, and 15.

Therefore, when a precoding matrix is transmitted by using a submode 2of a PUCCH mode 1-1, a 4-antenna codebook according to this embodimentis as good as a codebook of a 3GPP LTE R8; moreover, each precodingmatrix included in the 4-antenna codebook according to this embodimentof the present invention is applicable to a dual-polarized antenna. InTable C1, a total of 4 bits may be used to transmit the first precodingmatrix, where 3 bits represent the first PMI, i₁=I_(PMI1), and one bitis used to represent the second PMI, where i₂ and the second PMII_(PMI2) satisfy, for example, the following equation (8):i ₂=4×(I _(PMI1) mod 4)+└I _(PMI1)/4┘+2I _(PMI2)  (8)

where “mod” represents modulo, and “└ ┘” represents rounding down.

With reference to Table C1, it may be known that when a value range ofI_(PMI1) or i₁ is 0, a range of corresponding values of i₂ is (0, 2);when the value range of I_(PMI1) is 1, the range of corresponding valuesof i₂ is (4, 6); when the value range of I_(PMI1) is 2, the range ofcorresponding values of i₂ is (8, 10); when the value range of I_(PMI1)is 3, the range of corresponding values of i₂ is (12, 14); when thevalue range of I_(PMI1) is 4, the range of corresponding values of i₂ is(1, 3); when the value range of I_(PMI1) is 5, the range ofcorresponding values of i₂ is (5, 7); when the value range of I_(PMI1)is 6, the range of corresponding values of i₂ is (9, 11); and when thevalue range of I_(PMI1) is 7, the range of corresponding values of i₂ is(13, 15). That is, the value or value range of i₂ corresponding toI_(PMI2) is associated with the value or value range of i₁ correspondingto I_(PMI1).

Therefore, by means of the method for transmitting a 4-antenna precodingmatrix according to this embodiment, more precoding matrices that areapplicable to a uniform linear array antenna may be indicated duringcodebook subsampling without changing a feedback mode or feedback bits,and each precoding matrix in a codebook set after the subsampling isapplicable to a dual-polarized antenna, which may ensure thatperformance for application of the dual-polarized antenna is notaffected, improve system performance and enhance user experience.

In this embodiment, optionally, when the rank is determined to be 1, thefirst PMI, the second PMI, the first codebook index corresponding to thefirst PMI, and the second codebook index corresponding to the second PMIare determined according to Table C2:

TABLE C2 I_(PMI1) i₁ = I_(PMI1) + 8 I_(PMI2) i₂ 0 8 0 0 0 8 1 2 1 9 0 41 9 1 6 2 10 0 8 2 10 1 10 3 11 0 12 3 11 1 14 4 12 0 1 4 12 1 3 5 13 05 5 13 1 7 6 14 0 9 6 14 1 11 7 15 0 13 7 15 1 15where I_(PMI1) represents the first PMI, I_(PMI2) represents the secondPMI, i₁ represents the first codebook index, and i₂ represents thesecond codebook index.

It should be understood that, in Table C2, the second codebook index i₂and the second PMI I_(PMI2) satisfy, for example, the following equation(9):i ₂=4×((I _(PMI1)−8)mod 4)+└(I _(PMI1)−8)/4┘+2I _(PMI2)   (9)

where “mod” represents modulo, and “└ ┘” represents rounding down.

Similarly, in Table C2, there are a total of 8 DFT vectors; in thiscase, corresponding values of the second codebook index i₂ are 2, 3, 4,5, 10, 11, 12, and 13.

In this embodiment, optionally, when the rank is determined to be 1, thefirst PMI, the second PMI, the first codebook index corresponding to thefirst PMI, and the second codebook index corresponding to the second PMIare determined according to Table C3:

TABLE C3 I_(PMI1) i₁ = 2I_(PMI1) I_(PMI2) i₂ 0 0 0 0 0 0 1 2 1 2 0 8 1 21 10 2 4 0 1 2 4 1 3 3 6 0 9 3 6 1 11 4 8 0 0 4 8 1 2 5 10 0 8 5 10 1 106 12 0 1 6 12 1 3 7 14 0 9 7 14 1 11

where I_(PMI1) represents the first PMI, I_(PMI2) represents the secondPMI, i₁ represents the first codebook index, and i₂ represents thesecond codebook index.

With reference to Table 7, it may be known that when the first PMI, thesecond PMI, the first codebook index corresponding to the first PMI, andthe second codebook index corresponding to the second PMI have themutual relationships shown in Table C3, a codebook including 16precoding matrices on which subsampling is performed has a total of 8DFT vectors; in this case, as shown in Table C3, corresponding values ofthe second codebook index i₂ are 0, 1, 2, 3, 8, 9, 10, and

Therefore, when a precoding matrix is transmitted by using a submode 2of a PUCCH mode 1-1, a 4-antenna codebook according to this embodimentis as good as a codebook of a 3GPP LTE R8; moreover, each precodingmatrix included in the 4-antenna codebook according to this embodimentis applicable to a dual-polarized antenna. In Table C3, a total of 4bits may be used to transmit the first precoding matrix, where 3 bitsrepresent the first PMI, i₁=I_(PMI1), and one bit is used to representthe second PMI, where i₂ and the second PMI I_(PMI2) satisfy, forexample, the following equation (10):i ₂=8×((I _(PMI1) mod 4)mod 2)+└(I _(PMI1) mod 4)/2┘+2I _(PMI2)  (10)where “mod” represents modulo, and “└ ┘” represents rounding down.

With reference to Table C3, when a value range of I_(PMI1) is (0, 4), acorresponding value range of i₁ is (0, 8), and a corresponding valuerange of i₂ is (0, 2); when the value range of I_(PMI1) is (1, 5), thecorresponding value range of i₁ is (2, 10), and the corresponding valuerange of i₂ is (8, 10); when the value range of I_(PMI1) is (2, 6), thecorresponding value range of is (4, 12), and the corresponding valuerange of i₂ is (1, 3); when the value range of I_(PMI1) is (3, 7), thecorresponding value range of i₁ is (6, 14), and the corresponding valuerange of i₂ is (9, 11). That is, the value or value range of i₂corresponding to I_(PMI2) is associated with the value or value range ofi₁ corresponding to I_(PMI1).

In this embodiment, optionally, when the rank is determined to be 1, thefirst PMI, the second PMI, the first codebook index corresponding to thefirst PMI, and the second codebook index corresponding to the second PMIare determined according to Table C4:

TABLE C4 I_(PMI1) i₁ = 2I_(PMI1) + 1 I_(PMI2) i₂ 0 1 0 4 0 1 1 6 1 3 012 1 3 1 14 2 5 0 5 2 5 1 7 3 7 0 13 3 7 1 15 4 9 0 4 4 9 1 6 5 11 0 125 11 1 14 6 13 0 5 6 13 1 7 7 15 0 13 7 15 1 15

where I_(PMI1) represents the first PMI, I_(PMI2) represents the secondPMI, i₁ represents the first codebook index, and i₂ represents thesecond codebook index.

Similarly, in Table C4, there are a total of 8 DFT vectors; in thiscase, corresponding values of the second codebook index i₂ are 4, 5, 6,7, 12, 13, 14, and 15.

It should be understood that when the first PMI, the second PMI, thefirst codebook index corresponding to the first PMI, and the secondcodebook index corresponding to the second PMI have the mutualrelationships shown in Table C1, C2, C3, or C4, the precoding matrix Wdetermined according to the first codebook index i₁ and the secondcodebook index i₂ may be determined according to Table A, which is notdescribed herein any further for brevity.

It should be understood that the base station (eNB) may first configurea channel state information reference signal (“CSI-RS” for short) forthe UE. Specifically, with respect to Nt antennas or Nt antenna ports ofthe base station, the base station configures resources of antenna portsof Nt CSI-RSs for the UE, where Nt is a natural number, for example, Ntequals 4. In this case, the UE may measure channel quality oncorresponding CSI-RS resources, and may determine an RI, a PMI, a CQI,and the like that the UE wants the eNB to use when the base stationsends downlink data. After determining the channel state information(“CSI” for short) such as the RI, the PMI, and the CQI, the UE may feedback the CSI to the base station on a feedback resource configured bythe eNB for the UE. For example, a feedback mode configured by the eNBfor the UE is a submode 2 of a PUCCH mode 1-1; accordingly, the UE feedsback the RI on a subframe for feeding back the RI, and separately feedsback I_(PMI1), I_(PMI2), and the CQI on subframes for feeding back thefirst PMI I_(PMI1), the second PMI I_(PMI2), and the CQI, which is notdescribed herein any further for brevity.

It should be further understood that in this embodiment, the precodingmatrix set may be referred to as a codebook, and each precoding matrixin the precoding matrix set may be referred to as a code word; however,the present invention is not limited thereto.

It should be further understood that sequence numbers of the foregoingprocesses do not mean execution sequences in various embodiments. Theexecution sequences of the processes should be determined according tofunctions and internal logic of the processes, and should not beconstrued as any limitation on the implementation processes of theembodiments of the present invention.

Therefore, in the method for transmitting a 4-antenna precoding matrixaccording to this embodiment, the value range of the first codebookindex corresponding to the first PMI and the value range of the secondcodebook index corresponding to the second PMI have an associationrelationship, so that more precoding matrices that are applicable to auniform linear array antenna may be indicated during codebooksubsampling without changing a feedback mode or feedback bits, and eachprecoding matrix in a codebook set after the subsampling is applicableto a dual-polarized antenna, which may ensure that performance forapplication of the dual-polarized antenna is not affected, improvesystem performance and enhance user experience.

FIG. 2 shows a schematic flowchart of a method 20 for transmitting a4-antenna precoding matrix according to an embodiment. The method 20 maybe performed, for example, by a user equipment. As shown in FIG. 2, themethod 20 includes the following steps.

S21. Determine a rank used for indicating the number of transmissionlayers.

S22: Determine a value of a first codebook index corresponding to oneprecoding matrix set in a codebook set, where the codebook setcorresponds to the rank, and precoding matrices included in the codebookset are represented by the first codebook index and a second codebookindex.

S23: Determine a jointly coded value corresponding to the rank and thevalue of the first codebook index, where the jointly coded value and therank have a first correspondence, and the jointly coded value and thefirst codebook index have a second correspondence.

S24: Send the jointly coded value to a base station.

The precoding matrices W included in the codebook set satisfy thefollowing equation:

W=W₁×W₂, where

${W_{1} = \begin{bmatrix}X_{n} & 0 \\0 & X_{n}\end{bmatrix}},{X_{n} = \begin{bmatrix}1 & 1 & 1 & 1 \\q_{1}^{n} & q_{1}^{n + 8} & q_{1}^{n + 16} & q_{1}^{n + 24}\end{bmatrix}},$q₁=e^(j2π/32), and n=0, 1, . . . , 15; and

the first codebook index corresponds to one value of n, and a valuerange of n is a set {0, 1, 2, 3, 4, 5, 6, 7}, {8, 9, 10, 11, 12, 13, 14,15}, {0, 2, 4, 6}, {1, 3, 5, 7}, {8, 10, 12, 14}, or {9, 11, 13, 15}.

Therefore, the method for transmitting a 4-antenna precoding matrixaccording to this embodiment may prevent a problem where precodingmatrices are repeated after subsampling, thereby improving systemperformance and enhancing user experience.

In this embodiment, optionally, a value range of the first codebookindex i₁ is 0≦i₁≦15, and a value range of the second codebook index i₂is 0≦i₂≦L₂−1, where L₂ is a positive integer. For example, a value rangeof L₂ is 1≦L₂≦16, that is, the value range of the second codebook indexi₂ is, for example, 0≦i₂≦15.

In this embodiment, optionally, when the rank is determined to be 1, W₂satisfies the following equation (5):

$\begin{matrix}{W_{2} \in \left\{ {{\frac{1}{A}\begin{bmatrix}Y \\{{\alpha(i)}Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{j\;{\alpha(i)}Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{{- {\alpha(i)}}Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{{- j}\;{\alpha(i)}Y}\end{bmatrix}}} \right\}} & (5)\end{matrix}$

where Yε{e₁,e₂,e₃,e₄}, α(i)=q₁ ^(2(i-1)); when Y is e₁, α(i) is α(1);when Y is e₂, α(i) is α(2); when Y is e₃, α(i) is α(3); when Y is e₄,α(i) is α(4); e_(i) represents a column vector with a dimension of 4×1,where an i^(th) element in e_(i) is 1, all other elements are 0, andiε{1, 2, 3, 4}; A is a constant.

In this embodiment, optionally, when the rank determined by the UE is 2,W₂ satisfies the following equation (6):

$\begin{matrix}{W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ {\left( {e_{1},e_{1}} \right),\left( {e_{2},e_{2}} \right),\left( {e_{3},e_{3}} \right),\left( {e_{4},e_{4}} \right),\left( {e_{1},e_{2}} \right),\left( {e_{2},e_{3}} \right),\left( {e_{1},e_{4}} \right),\left( {e_{2},e_{4}} \right)} \right\}} & (6)\end{matrix}$

where e_(i) represents a column vector with a dimension of 4×1, ani^(th) element in e_(i) is 1, all other elements are 0, and iε{1, 2, 3,4}; B is a constant.

In this embodiment, optionally, when the rank is determined to be 2, W₂satisfies the following equation (7):

$\begin{matrix}{{W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & Y_{2}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{- Y_{1}} & Y_{2}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{- Y_{1}} & {- Y_{2}}\end{bmatrix}}} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ \left( {e_{2},e_{4}} \right) \right\}}{W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ {\left( {e_{1},e_{1}} \right),\left( {e_{2},e_{2}} \right),\left( {e_{3},e_{3}} \right),\left( {e_{4},e_{4}} \right)} \right\}}{W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{2} & {- Y_{1}}\end{bmatrix}},} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ {\left( {e_{1},e_{3}} \right),\left( {e_{2},e_{4}} \right),\left( {e_{3},e_{1}} \right),\left( {e_{4},e_{2}} \right)} \right\}}} & (7)\end{matrix}$

where e_(i) represents a column vector with a dimension of 4×1, ani^(th) element in e_(i) is 1, all other elements are 0, and iε{1, 2, 3,4}; B is a constant.

That is, in this embodiment, when the user equipment determines that therank used for indicating the number of transmission layers is 2, W₂satisfies the equation (6) or W₂ satisfies the equation (7).

In this embodiment, if a 4-antenna codebook is transmitted in a submode1 of a PUCCH mode 1-1, a solution used for jointly coding the rank RIand i₁ needs to be designed. When the rank is 2, the 4-antenna codebookthat is determined according to Table B1 (corresponding to the equation(6)) or Table B2 (corresponding to the equation (7)) includes manyrepeated precoding matrices.

Specifically, for a solution (hereinafter referred to as solution 1 forshort) represented by the equation (6) and a solution (hereinafterreferred to as solution 2 for short) represented by the equation (7), W₁satisfies the following equation:

${W_{1} = \begin{bmatrix}X_{n} & 0 \\0 & X_{n}\end{bmatrix}},{X_{n} = \begin{bmatrix}1 & 1 & 1 & 1 \\q_{1}^{n} & q_{1}^{n + 8} & q_{1}^{n + 16} & q_{1}^{n + 24}\end{bmatrix}},$and q₁=e^(j2π/32) (n=0, 1, . . . , 15)

Accordingly, four beam directions or column vectors included in X_(n)and X_(n+8) (in this case, n=0 to 7) are the same. For example, when

$X_{0} = \begin{bmatrix}1 & 1 & 1 & 1 \\e^{j\; 2\pi\frac{0}{32}} & e^{j\; 2\pi\frac{8}{32}} & e^{j\; 2\pi\frac{16}{32}} & e^{j\; 2\pi\frac{24}{32}}\end{bmatrix}$and

${X_{8} = \begin{bmatrix}1 & 1 & 1 & 1 \\e^{j\; 2\pi\frac{8}{32}} & e^{j\; 2\pi\frac{16}{32}} & e^{j\; 2\pi\frac{24}{32}} & e^{j\; 2\pi\frac{0}{32}}\end{bmatrix}},$it is obvious that beam directions or column vectors included in X₀ andX₈ are the same, and only sequences of the column vectors are different.As a result, some code words are repeated in a codebook generated basedon W=W₁·W₂ when the rank is 2. The problem where some code words arerepeated exists in both solution 1 and solution 2.

As an example, for both solution 1 and solution 2, W₂ satisfies thefollowing equation:

${W_{2} \in \left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}} \right\}},$

where (Y₁, Y₂)=(e_(i),e_(k))ε{(e₁,e₁),(e₂,e₂),(e₃,e₃),(e₄,e₄)}, e_(i)and e_(k) represent one column vector with a dimension of 4×1, an i^(th)element in e_(i) is 1, and all other elements are 0.

When n=0 and (Y₁, Y₂)=(e₂,e₂),

${W = {{W_{1} \cdot W_{2}} = {{{\frac{1}{B}\begin{bmatrix}X_{n} & 0 \\0 & X_{n}\end{bmatrix}} \cdot \begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}} = \begin{bmatrix}1 & 1 \\e^{j\; 2\pi\;\frac{8}{32}} & e^{j\; 2\pi\;\frac{8}{32}} \\\begin{pmatrix}1 \\e^{j\; 2\pi\;\frac{8}{32}}\end{pmatrix} & {- \begin{pmatrix}1 \\e^{j\; 2\pi\;\frac{8}{32}}\end{pmatrix}}\end{bmatrix}}}};$and

when n=8 and (Y₁, Y₂)=(e₁,e₁),

$W = {{W_{1} \cdot W_{2}} = {{{\frac{1}{B}\begin{bmatrix}X_{n} & 0 \\0 & X_{n}\end{bmatrix}} \cdot \begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}} = {\begin{bmatrix}1 & 1 \\e^{j\; 2\pi\;\frac{8}{32}} & e^{j\; 2\pi\;\frac{8}{32}} \\\begin{pmatrix}1 \\e^{j\; 2\pi\;\frac{8}{32}}\end{pmatrix} & {- \begin{pmatrix}1 \\e^{j\; 2\pi\;\frac{8}{32}}\end{pmatrix}}\end{bmatrix}.}}}$

It is obvious that two code words represented when n is equal to 0 and nis equal to 8 are identical. A large amount of repeated code words mayreduce efficiency of the codebook, so that system performancedeteriorates. Therefore, when subsampling is performed on the codebook,it is required that the codebook after the subsampling is performedshould not include repeated code words or repeated precoding matrices.It should be understood that the foregoing analysis is not limited tothis embodiment.

In R12, a 4-antenna codebook whose rank is 3 or 4 is a codebook in R8.Therefore, with respect to a codebook whose rank is 3 or 4, W₁corresponding to i₁ is an identity matrix and does not need to berepresented by a bit. When the rank and the PMI of the precoding matrixare transmitted in the submode 1 of the PUCCH mode 1-1, the rank and i₁are jointly coded, and subsampling is performed on i₁; however,subsampling is not performed on i₂ in this case.

With respect to a codebook whose rank is 2, if i₁ is represented bythree bits after subsampling, it is required that a value range of n inX_(n) corresponding to i₁ on which the subsampling is performed is 0-7or 8-15, and it is not required that the value range of n is 0, 2, 4, 6,8, 10, 12, 14 or 1, 3, 5, 7, 9, 11, 13, 15. This may prevent occurrenceof repeated matrices. Moreover, with respect to a codebook whose rank is1, the value range of n in X_(n) is 0-7 or 8-15 and may include alldirections, so as to be the same as the value range in a situation inwhich the rank is 2.

With respect to a codebook whose rank is 1 or 2, if four states of i₁are represented by two bits after subsampling is performed on i₁, atotal of PUCCH resources of three bits are required to represent aprecoding matrix. In this case, it is required that n in X_(n)corresponding to i₁ after the subsampling is performed is (0, 2, 4, 6),(1, 3, 5, 7), (8, 10, 12, 14), or (9, 11, 13, 15). In this case, for allvectors in X_(n) space and beam directions may be divided evenly.

In addition, with respect to the codebook whose rank is 1 or 2, if thenumber of states after the subsampling is performed on i₁ is not 2raised to the power of x (x is an integer), it should be prevented asmuch as possible that n and n+8 corresponding to i₁ concurrently exist.For example, when the number Z of states after the subsampling isperformed on i₁ satisfies 8>Z>4 and Y is an integer, the value range ofn is Z values in (0, 2, 4, 6, 8, 10, 12, 14) or Z values in (1, 3, 5, 7,9, 11, 13, 15).

One vector [1 q₁ ^(x)]^(T) in X_(n) represents one direction, which maybe represented by x, where x is an integer and a value range of x is 0to 31. Because q₁=e^(j2π/32), q₁ ^(x)=q₁ ^(x+32). For example, when thevalue range of n is (0, 2, 4, 6), all directions (vectors) in X_(n) arerepresented by x, which may be 16 directions: 0, 2, 4, 6, 8, 10, 12, 14,16, 18, 20, 22, 24, 26, 28; therefore, space may be divided evenly.

Specifically, in this embodiment of the present invention, optionally,when the number of bits bearing the jointly coded value is 4, thecorrespondence between the jointly coded value and the rank and thecorrespondence between the jointly coded value and the first codebookindex are determined according to the following Table D:

TABLE D I_(RI/PMI1) RI i₁ 0-7 1 I_(RI/PMI1)  8-15 2 I_(RI/PMI1) − 8

where I_(RI/PMI1) represents the jointly coded value, RI represents therank, and i₁ represents the first codebook index.

Optionally, in this embodiment, when the number of bits bearing thejointly coded value is 3, the correspondence between the jointly codedvalue and the rank and the correspondence between the jointly codedvalue and the first codebook index are determined according to thefollowing Table E:

TABLE E I_(RI/PMI1) RI i₁ 0-3 1 2 × I_(RI/PMI1) 4-7 2 2 × (I_(RI/PMI1) −4)

where I_(RI/PMI1) represents the jointly coded value, RI represents therank, and i₁ represents the first codebook index.

It should be understood that in this embodiment, when the rank isdetermined to be 1, the precoding matrices W included in the codebookset are determined according to Table A:

TABLE A i₂ i₁ 0 1 2 3 0-15 W_(i) ₁ _(,0) ⁽¹⁾ W_(i) ₁ _(,1) ⁽¹⁾ W_(i) ₁_(,2) ⁽¹⁾ W_(i) ₁ _(,3) ⁽¹⁾ i₂ i₁ 4 5 6 7 0-15 W_(i) ₁ _(+8,0) ⁽¹⁾ W_(i)₁ _(+8,1) ⁽¹⁾ W_(i) ₁ _(+8,2) ⁽¹⁾ W_(i) ₁ _(+8,3) ⁽¹⁾ i₂ i₁ 8 9 10 110-15 W_(i) ₁ _(+16,0) ⁽¹⁾ W_(i) ₁ _(+16,1) ⁽¹⁾ W_(i) ₁ _(+16,2) ⁽¹⁾W_(i) ₁ _(+16,3) ⁽¹⁾ i₂ i₁ 12 13 14 15 0-15 W_(i) ₁ _(+24,0) ⁽¹⁾ W_(i) ₁_(+24,1) ⁽¹⁾ W_(i) ₁ _(+24,2) ⁽¹⁾ W_(i) ₁ _(+24,3) ⁽¹⁾

where

${W_{m,k}^{(1)} = {\frac{1}{2}\begin{bmatrix}v_{m} \\{\varphi_{k}{\gamma(m)}v_{m}}\end{bmatrix}}},{{\gamma(m)} = e^{j\; 2\pi\frac{{({m - i_{1}})}/4}{32}}},{v_{m} = \begin{bmatrix}1 & e^{j\; 2\pi\;{m/32}}\end{bmatrix}},$φ_(k)=e^(jπk/2), and m and k are nonnegative integers; i₁ represents thefirst codebook index; i₂ represents the second codebook index.

It should be further understood that in this embodiment, when the rankdetermined by the UE is 2, the precoding matrices W included in thecodebook set are determined according to Table B1 or B2:

TABLE B1 i₂ i₁ 0 1 2 3 0-15 W_(i) ₁ _(,i) ₁ _(,0) ⁽²⁾ W_(i) ₁ _(,i) ₁_(,1) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+8,0) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+8,1) ⁽²⁾ i₂i₁ 4 5 6 7 0-15 W_(i) ₁ _(+16,i) ₁ _(+16,0) ⁽²⁾ W_(i) ₁ _(+16,i) ₁_(+16,1) ⁽²⁾ W_(i) ₁ _(+24,i) ₁ _(+24,0) ⁽²⁾ W_(i) ₁ _(+24,i) ₁ _(+24,1)⁽²⁾ i₂ i₁ 8 9 10 11 0-15 W_(i) ₁ _(,i) ₁ _(+8,0) ⁽²⁾ W_(i) ₁ _(,i) ₁_(+8,1) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+16,0) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+16,1)⁽²⁾ i₂ i₁ 12 13 14 15 0-15 W_(i) ₁ _(,i) ₁ _(+24,0) ⁽²⁾ W_(i) ₁ _(,i) ₁_(+24,1) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+24,0) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+24,1)⁽²⁾

TABLE B2 i₂ i₁ 0 1 2 3 0-15 W_(i) ₁ _(,i) ₁ _(,0) ⁽²⁾ W_(i) ₁ _(,i) ₁_(,1) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+8,0) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+8,1) ⁽²⁾ i₂i₁ 4 5 6 7 0-15 W_(i) ₁ _(+16,i) ₁ _(+16,0) ⁽²⁾ W_(i) ₁ _(+16,i) ₁_(+16,1) ⁽²⁾ W_(i) ₁ _(+24,i) ₁ _(+24,0) ⁽²⁾ W_(i) ₁ _(+24,i) ₁ _(+24,1)⁽²⁾ i₂ i₁ 8 9 10 11 0-15 {tilde over (W)}_(i) ₁ _(+8,i) ₁ _(+24,0) ⁽²⁾W_(i) ₁ _(+8,i) ₁ _(+24,0) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+24,2) ⁽²⁾ {tildeover (W)}_(i) ₁ _(+8,i) ₁ _(+24,2) ⁽²⁾ i₂ i₁ 12 13 14 15 0-15

where

${W_{m,m^{\prime},k}^{(2)} = {\frac{1}{\sqrt{8}}\begin{bmatrix}v_{m} & v_{m^{\prime}} \\{\varphi_{k}v_{m}} & {{- \varphi_{k}}v_{m^{\prime}}}\end{bmatrix}}},{{\overset{\sim}{W}}_{m,m^{\prime},k}^{(2)} = {\frac{1}{\sqrt{8}}\begin{bmatrix}v_{m} & v_{m^{\prime}} \\{\varphi_{k}v_{m}} & {\varphi_{k}v_{m^{\prime}}}\end{bmatrix}}},{{\overset{\overset{\sim}{\sim}}{W}}_{m,m^{\prime},k}^{(2)} = {\frac{1}{\sqrt{8}}\begin{bmatrix}v_{m} & v_{m^{\prime}} \\{\varphi_{k}v_{m^{\prime}}} & {{- \varphi_{k}}v_{m}}\end{bmatrix}}},{v_{m} = \begin{bmatrix}1 & e^{j\; 2\pi\;{m/32}}\end{bmatrix}},{v_{m^{\prime}} = \begin{bmatrix}1 & e^{j\; 2\pi\;{m^{\prime}/32}}\end{bmatrix}},$φ_(k)=e^(jπk/2), and m, m′, and k are nonnegative integers; i₁represents the first codebook index; i₂ represents the second codebookindex.

It should be understood that in this embodiment, the jointly coded valuerepresents a value generated by performing joint coding on the rank anda first PMI, which is not described herein any further for brevity.

It should be further understood that sequence numbers of the foregoingprocesses do not mean execution sequences in various embodiments. Theexecution sequences of the processes should be determined according tofunctions and internal logic of the processes, and should not beconstrued as any limitation on the implementation processes of theembodiments.

Therefore, when a precoding matrix is transmitted in the submode 1 ofthe PUCCH mode 1-1, the method for transmitting a 4-antenna precodingmatrix according to this embodiment of the present invention may preventa problem where precoding matrices are repeated after subsampling,thereby improving system performance and enhancing user experience.

FIG. 3 shows a schematic flowchart of a method 30 for transmitting a4-antenna precoding matrix according to an embodiment. The method 30 maybe performed, for example, by a user equipment. As shown in FIG. 3, themethod 30 includes the following steps.

S31. Determine a rank used for indicating the number of transmissionlayers.

S32. Determine a first precoding matrix in a codebook set correspondingto the rank, where precoding matrices included in the codebook set arerepresented by a first codebook index and a second codebook index.

S33: Determine a second precoding matrix indicator PMI used forindicating the first precoding matrix, where the second PMI and thesecond codebook index have a first correspondence, and for one givenfirst codebook index, a value range of the second codebook indexcorresponding to a value range of the second PMI is a proper subset of avalue range of the second codebook index.

S34: Send the second PMI used for indicating the first precoding matrixto a base station.

The precoding matrices W included in the codebook set satisfy thefollowing equation:

W=W₁×W₂, where

${W_{1} = \begin{bmatrix}X_{n} & 0 \\0 & X_{n}\end{bmatrix}},{X_{n} = \begin{bmatrix}1 & 1 & 1 & 1 \\q_{1}^{n} & q_{1}^{n + 8} & q_{1}^{n + 16} & q_{1}^{n + 24}\end{bmatrix}},$q₁=e^(j2π/32),and n=0, 1, . . . , 15;

the first codebook index corresponds to one value of n, and a valuerange of n is a set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14,15}; and

when the rank is determined to be 2, in precoding matrix sets that aredetermined according to the first codebook index and the second codebookindex corresponding to the value range of the second PMI, a firstprecoding matrix set corresponding to a first codebook index i_(1,a) anda second precoding matrix set corresponding to a first codebook indexi_(1,a+8) are mutually exclusive, where the first codebook index i_(1,a)represents a first codebook index corresponding to n whose value is a,the first codebook index i_(1,a+8) represents a first codebook indexcorresponding to n whose value is a+8, and aε{0, 1, 2, 3, 4, 5, 6, 7}.

In a case that a precoding matrix is transmitted in a PUCCH mode 2-1,when the rank is 1, subsampling is not performed on a codebook; when therank is 2, the subsampling is not performed on the first codebook index,but the subsampling is performed on the second codebook index, and thesecond codebook index is represented not by the original four bits, butby two bits after the subsampling.

Therefore, the method for transmitting a 4-antenna precoding matrixaccording to this embodiment of the present invention may prevent aproblem where precoding matrices are repeated after subsampling, therebyimproving system performance and enhancing user experience.

In this embodiment, optionally, a value range of the first codebookindex i₁ is 0≦i₁≦15, and a value range of the second codebook index i₂is 0≦i₂≦L₂−1, where L₂ is a positive integer. For example, a value rangeof L₂ is 1≦L₂≦16, that is, the value range of the second codebook indexi₂ is, for example, 0≦i₂≦15.

In this embodiment, optionally, when the rank is determined to be 1, W₂satisfies the following equation (5):

$\begin{matrix}{W_{2} \in \left\{ {{\frac{1}{A}\begin{bmatrix}Y \\{{\alpha(i)}Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{j\;{\alpha(i)}Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{{- {\alpha(i)}}Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{{- j}\;{\alpha(i)}Y}\end{bmatrix}}} \right\}} & (5)\end{matrix}$

where Yε{e₁,e₂,e₃,e₄}, α(i)=q₁ ^(2(i-1)); when Y is e₁, α(i) is α(1);when Y is e₂, α(i) is α(2); when Y is e₃, α(i) is α(3); when Y is e₄,α(i) is α(4); e_(i) represents a column vector with a dimension of 4×1,where an i^(th) element in e_(i) is 1, all other elements are 0, andiε{1, 2, 3, 4}; A is a constant.

In this embodiment, optionally, when the rank determined by the UE is 2,W₂ satisfies the following equation (6):

$\begin{matrix}{W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ {\left( {e_{1},e_{1}} \right),\left( {e_{2},e_{2}} \right),\left( {e_{3},e_{3}} \right),\left( {e_{4},e_{4}} \right),\left( {e_{1},e_{2}} \right),\left( {e_{2},e_{3}} \right),\left( {e_{1},e_{4}} \right),\left( {e_{2},e_{4}} \right)} \right\}} & (6)\end{matrix}$

where e_(i) represents a column vector with a dimension of 4×1, ani^(th) element in e_(i) is 1, all other elements are 0, and iε{1, 2, 3,4}; B is a constant.

In this embodiment, optionally, when the rank is determined to be 2, W₂satisfies the following equation (7):

$\begin{matrix}{{W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & Y_{2}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{- Y_{1}} & Y_{2}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{- Y_{1}} & {- Y_{2}}\end{bmatrix}}} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ \left( {e_{2},e_{4}} \right) \right\}}{W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ {\left( {e_{1},e_{1}} \right),\left( {e_{2},e_{2}} \right),\left( {e_{3},e_{3}} \right),\left( {e_{4},e_{4}} \right)} \right\}}{W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{2} & {- Y_{1}}\end{bmatrix}},} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ {\left( {e_{1},e_{3}} \right),\left( {e_{2},e_{4}} \right),\left( {e_{3},e_{1}} \right),\left( {e_{4},e_{2}} \right)} \right\}}} & (7)\end{matrix}$

where e_(i) represents a column vector with a dimension of 4×1, ani^(th) element in e_(i) is 1, all other elements are 0, and iε{1, 2, 3,4}; B is a constant.

That is, in this embodiment, when the user equipment determines that therank used for indicating the number of transmission layers is 2, W₂satisfies the equation (6) or W₂ satisfies the equation (7).

In this embodiment, in order to prevent a problem where code words areoverlapped, optionally, when the rank is determined to be 2, mutualrelationships between the second PMI, the first codebook index, and thesecond codebook index are determined according to Table F1 or F2:

TABLE F1 I_(PMI2) i₁ i₂ 0-3 0-7 2 × I_(PMI2)  8-15 2 × I_(PMI2) + 1

TABLE F2 I_(PMI2) i₁ i₂ 0-3 0-7 2 × I_(PMI2)  8-15 2 × I_(PMI2) + 8

where I_(PMI2) represents the second PMI, i₁ represents the firstcodebook index, and i₂ represents the second codebook index.

Therefore, by means of the method for transmitting a 4-antenna precodingmatrix according to this embodiment, more precoding matrices that areapplicable to a uniform linear array antenna may be indicated withoutchanging a feedback mode or feedback bits, and it may also be ensuredthat performance for application of a dual-polarized antenna is notaffected, and the problem where code words are overlapped aftersubsampling may be prevented, so that system performance may be improvedand user experience may be enhanced.

In this embodiment, optionally, when the rank is determined to be 3 or4, the precoding matrices included in the codebook set corresponding tothe rank are:

four precoding matrices with codebook indexes 0 to 3 in Table G; or

four precoding matrices with codebook indexes 4 to 7 in Table G; or

four precoding matrices with codebook indexes 12 to 15 in Table G,

TABLE G Codebook RI Index u_(n) 1 2 3 4 0 u₀ = [1 −1 −1 −1]^(T) W₀^({1}) W₀ ^({14})/{square root over (2)} W₀ ^({124})/{square root over(3)} W₀ ^({1234})/2 1 u₁ = [1 −j 1 j]^(T) W₁ ^({1}) W₁ ^({12})/{squareroot over (2)} W₁ ^({123})/{square root over (3)} W₁ ^({1234})/2 2 u₂ =[1 1 −1 1]^(T) W₂ ^({1}) W₂ ^({12})/{square root over (2)} W₂^({123})/{square root over (3)} W₂ ^({3214})/2 3 u₃ = [1 j 1 −j]^(T) W₃^({1}) W₃ ^({12})/{square root over (2)} W₃ ^({123})/{square root over(3)} W₃ ^({3214})/2 4 u₄ = [1 (−1 − j)/{square root over (2)} −j (1 −j)/{square root over (2)}]^(T) W₄ ^({1}) W₄ ^({14})/{square root over(2)} W₄ ^({124})/{square root over (3)} W₄ ^({1234})/2 5 u₅ = [1 (1 −j)/{square root over (2)} j (−1 − j)/{square root over (2)}]^(T) W₅^({1}) W₅ ^({14})/{square root over (2)} W₅ ^({124})/{square root over(3)} W₅ ^({1234})/2 6 u₆ = [1 (1 + j)/{square root over (2)} −j (−1 +j)/{square root over (2)}]^(T) W₆ ^({1}) W₆ ^({13})/{square root over(2)} W₆ ^({134})/{square root over (3)} W₆ ^({1324})/2 7 u₇ = [1 (−1 +j)/{square root over (2)} j (1 + j)/{square root over (2)}]^(T) W₇^({1}) W₇ ^({13})/{square root over (2)} W₇ ^({134})/{square root over(3)} W₇ ^({1324})/2 8 u₈ = [1 −1 1 1]^(T) W₈ ^({1}) W₈ ^({12})/{squareroot over (2)} W₈ ^({124})/{square root over (3)} W₈ ^({1234})/2 9 u₉ =[1 −j −1 −j]^(T) W₉ ^({1}) W₉ ^({14})/{square root over (2)} W₉^({134})/{square root over (3)} W₉ ^({1234})/2 10 u₁₀ = [1 1 1 −1]^(T)W₁₀ ^({1}) W₁₀ ^({13})/{square root over (2)} W₁₀ ^({123})/{square rootover (3)} W₁₀ ^({1324})/2 11 u₁₁ = [1 j −1 j]^(T) W₁₁ ^({1}) W₁₁^({13})/{square root over (2)} W₁₁ ^({134})/{square root over (3)} W₁₁^({1324})/2 12 u₁₂ = [1 −1 −1 1]^(T) W₁₂ ^({1}) W₁₂ ^({12})/{square rootover (2)} W₁₂ ^({123})/{square root over (3)} W₁₂ ^({1234})/2 13 u₁₃ =[1 −1 1 −1]^(T) W₁₃ ^({1}) W₁₃ ^({13})/{square root over (2)} W₁₃^({123})/{square root over (3)} W₁₃ ^({1324})/2 14 u₁₄ = [1 1 −1 −1]^(T)W₁₄ ^({1}) W₁₄ ^({13})/{square root over (2)} W₁₄ ^({123})/{square rootover (3)} W₁₄ ^({3214})/2 15 u₁₅ = [1 1 1 1]^(T) W₁₅ ^({1}) W₁₅^({12})/{square root over (2)} W₁₅ ^({123})/{square root over (3)} W₁₅^({1234})/2

where W_(n) ^({s}) represents a matrix formed by a column set {s} of amatrix W_(n)=I−2u_(n)u_(n) ^(H)/u_(n) ^(H)u_(n), and I is a 4×4 identitymatrix.

Specifically, when the rank is determined to be 3 or 4 and the precodingmatrices included in the codebook set corresponding to the rank are thefour precoding matrices with the codebook indexes 0 to 3 or 4 to 7 inTable G, if rank fallback is performed and the rank falls back to therank 1, four uniform DFT vectors may be obtained. These DFT vectors areapplicable to a ULA antenna, and the four DFT vectors are alsoapplicable to a dual-polarized antenna.

When the rank is determined to be 3 or 4 and the precoding matricesincluded in the codebook set corresponding to the rank are the fourprecoding matrices with the codebook indexes 12 to 15 in Table G, thefour precoding matrices are open-loop precoding matrices, and the fourprecoding matrices have a large chordal distance.

It should be understood that in this embodiment, when the rank isdetermined to be 1, the precoding matrices W included in the codebookset are determined according to Table A:

TABLE A i₂ i₁ 0 1 2 3 0-15 W_(i) ₁ _(,0) ⁽¹⁾ W_(i) ₁ _(,1) ⁽¹⁾ W_(i) ₁_(,2) ⁽¹⁾ W_(i) ₁ _(,3) ⁽¹⁾ i₂ i₁ 4 5 6 7 0-15 W_(i) ₁ _(+8,0) ⁽¹⁾ W_(i)₁ _(+8,1) ⁽¹⁾ W_(i) ₁ _(+8,2) ⁽¹⁾ W_(i) ₁ _(+8,3) ⁽¹⁾ i₂ i₁ 8 9 10 110-15 W_(i) ₁ _(+16,0) ⁽¹⁾ W_(i) ₁ _(+16,1) ⁽¹⁾ W_(i) ₁ _(+16,2) ⁽¹⁾W_(i) ₁ _(+16,3) ⁽¹⁾ i₂ i₁ 12 13 14 15 0-15 W_(i) ₁ _(+24,0) ⁽¹⁾ W_(i) ₁_(+24,1) ⁽¹⁾ W_(i) ₁ _(+24,2) ⁽¹⁾ W_(i) ₁ _(+24,3) ⁽¹⁾

where

${W_{m,k}^{(1)} = {\frac{1}{2}\begin{bmatrix}v_{m} \\{\varphi_{k}{\gamma(m)}v_{m}}\end{bmatrix}}},{{\gamma(m)} = e^{j\; 2\pi\frac{{({m - i_{1}})}/4}{32}}},{v_{m} = \begin{bmatrix}1 & e^{j\; 2\pi\;{m/32}}\end{bmatrix}},$φ_(k)=e^(jπk/2), and m and k are nonnegative integers; i₁ represents thefirst codebook index; i₂ represents the second codebook index.

It should be further understood that in this embodiment, when the rankdetermined by the UE is 2, the precoding matrices W included in thecodebook set are determined according to Table B1 or B2:

TABLE B1 i₂ i₁ 0 1 2 3 0-15 W_(i) ₁ _(,i) ₁ _(,0) ⁽²⁾ W_(i) ₁ _(,i) ₁_(,1) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+8,0) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+8,1) ⁽²⁾ i₂i₁ 4 5 6 7 0-15 W_(i) ₁ _(+16,i) ₁ _(+16,0) ⁽²⁾ W_(i) ₁ _(+16,i) ₁_(+16,1) ⁽²⁾ W_(i) ₁ _(+24,i) ₁ _(+24,0) ⁽²⁾ W_(i) ₁ _(+24,i) ₁ _(+24,1)⁽²⁾ i₂ i₁ 8 9 10 11 0-15 W_(i) ₁ _(,i) ₁ _(+8,0) ⁽²⁾ W_(i) ₁ _(,i) ₁_(+8,1) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+16,0) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+16,1)⁽²⁾ i₂ i₁ 12 13 14 15 0-15 W_(i) ₁ _(,i) ₁ _(+24,0) ⁽²⁾ W_(i) ₁ _(,i) ₁_(+24,1) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+24,0) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+24,1)⁽²⁾

TABLE B2 i₂ i₁ 0 1 2 3 0-15 W_(i) ₁ _(,i) ₁ _(,0) ⁽²⁾ W_(i) ₁ _(,i) ₁_(,1) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+8,0) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+8,1) ⁽²⁾ i₂i₁ 4 5 6 7 0-15 W_(i) ₁ _(+16,i) ₁ _(+16,0) ⁽²⁾ W_(i) ₁ _(+16,i) ₁_(+16,1) ⁽²⁾ W_(i) ₁ _(+24,i) ₁ _(+24,0) ⁽²⁾ W_(i) ₁ _(+24,i) ₁ _(+24,1)⁽²⁾ i₂ i₁ 8 9 10 11 0-15 {tilde over (W)}_(i) ₁ _(+8,i) ₁ _(+24,0) ⁽²⁾W_(i) ₁ _(+8,i) ₁ _(+24,0) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+24,2) ⁽²⁾ {tildeover (W)}_(i) ₁ _(+8,i) ₁ _(+24,2) ⁽²⁾ i₂ i₁ 12 13 14 15 0-15

where

${W_{m,m^{\prime},k}^{(2)} = {\frac{1}{\sqrt{8}}\begin{bmatrix}v_{m} & v_{m^{\prime}} \\{\varphi_{k}v_{m}} & {{- \varphi_{k}}v_{m^{\prime}}}\end{bmatrix}}},{{\overset{\sim}{W}}_{m,m^{\prime},k}^{(2)} = {\frac{1}{\sqrt{8}}\begin{bmatrix}v_{m} & v_{m^{\prime}} \\{\varphi_{k}v_{m}} & {\varphi_{k}v_{m^{\prime}}}\end{bmatrix}}},{{\overset{\overset{\sim}{\sim}}{W}}_{m,m^{\prime},k}^{(2)} = {\frac{1}{\sqrt{8}}\begin{bmatrix}v_{m} & v_{m^{\prime}} \\{\varphi_{k}v_{m^{\prime}}} & {{- \varphi_{k}}v_{m}}\end{bmatrix}}},{v_{m} = \begin{bmatrix}1 & e^{j\; 2\pi\;{m/32}}\end{bmatrix}},{v_{m^{\prime}} = \begin{bmatrix}1 & e^{j\; 2\pi\;{m^{\prime}/32}}\end{bmatrix}},$φ_(k)=e^(jπk/2), and k are nonnegative integers; i₁ represents the firstcodebook index; i₂ represents the second codebook index.

It should be further understood that sequence numbers of the foregoingprocesses do not mean execution sequences in various embodiments. Theexecution sequences of the processes should be determined according tofunctions and internal logic of the processes, and should not beconstrued as any limitation on the implementation processes of theembodiments.

Therefore, when a precoding matrix is transmitted in the PUCCH mode 2-1,the method for transmitting a 4-antenna precoding matrix according tothis embodiment may prevent a problem where precoding matrices arerepeated after subsampling, thereby improving system performance andenhancing user experience.

The methods for transmitting a 4-antenna precoding matrix according tothe embodiments are described in detail above based on a user equipmentwith reference to FIG. 1 to FIG. 3. The following describes methods fortransmitting a 4-antenna precoding matrix according to the embodimentsbased on a base station with reference to FIG. 4 to FIG. 6.

As shown in FIG. 4, a method 60 for transmitting a 4-antenna precodingmatrix according to an embodiment may be performed by as base station.The method 60 includes the following steps.

S61: Receive a rank used for indicating the number of transmissionlayers, a first precoding matrix indicator PMI, and a second PMI thatare sent by a user equipment.

S62: Determine a first precoding matrix in a codebook set correspondingto the rank according to the first PMI and the second PMI, whereprecoding matrices included in the codebook set are represented by afirst codebook index and a second codebook index, the first PMI and thefirst codebook index have a first correspondence, and the second PMI andthe second codebook index have a second correspondence.

The precoding matrices W included in the codebook set satisfy thefollowing equation:

W=W₁×W₂, where

${W_{1} = \begin{bmatrix}X_{n} & 0 \\0 & X_{n}\end{bmatrix}},{X_{n} = \begin{bmatrix}1 & 1 & 1 & 1 \\q_{1}^{n} & q_{1}^{n + 8} & q_{1}^{n + 16} & q_{1}^{n + 24}\end{bmatrix}},$q₁=e^(j2π/32), and n=0, 1, . . . , 15; and

the first codebook index corresponds to one value of n, and a valuerange of n is a set {0, 1, 2, 3, 4, 5, 6, 7}, {8, 9, 10, 11, 12, 13, 14,15}, {0, 2, 4, 6, 8, 10, 12, 14}, or {1, 3, 5, 7, 9, 11, 13, 15}.

Therefore, by means of the method for transmitting a 4-antenna precodingmatrix according to this embodiment, more precoding matrices that areapplicable to a uniform linear array antenna may be indicated withoutchanging a feedback mode or feedback bits, and it may also be ensuredthat performance for application of a dual-polarized antenna is notaffected, so that system performance may be improved and user experiencemay be enhanced.

It should be understood that in this embodiment, the base station mayreceive, by means of CSI information sent by the UE, the PMI sent by theUE, where the CSI information may further include an RI, a CQI, and thelike. The base station may obtain, according to the RI and the PMI, theprecoding matrix fed back by the UE, and may obtain, according to theCQI, channel quality when the precoding matrix is used. When the basestation performs single-user MIMO transmission for the UE, the basestation may perform precoding on downlink data of the UE by using theprecoding matrix, and may determine, according to the CQI, a modulationand coding scheme for sending the downlink data. When the base stationperforms multi-user MIMO transmission for the UE, for example,multi-user MIMO for two users, the base station may obtain, according tothe precoding matrix fed back by the UE and a precoding matrix fed backby a pairing UE and by using a zero forcing (“ZF” for short) method, aprecoding matrix that eliminates multi-user interference. Therefore, theeNB may perform precoding on the downlink data of the multi-user MIMO byusing the precoding matrix; moreover, the base station may determine,according to CQIs fed back by the two users, a modulation and codingscheme for performing the multi-user MIMO transmission for the twousers, which is not described herein any further for brevity.

In this embodiment, optionally, when the received rank is 1, W₂satisfies the following equation:

${W_{2} \in \left\{ {{\frac{1}{A}\begin{bmatrix}Y \\{{\alpha(i)}Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{j\;{\alpha(i)}T}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{{- {\alpha(i)}}Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{{- j}\;{\alpha(i)}Y}\end{bmatrix}}} \right\}},$

where Yε{e₁,e₂,e₃,e₄}, α(i)=q₁ ^(2(i-1)); when Y is e₁, α(i) is α(1);when Y is e₂, α(i) is α(2); when Y is e₃, α(i) is α(3); when Y is e₄,α(i) is α(4); e_(i) represents a column vector with a dimension of 4×1,where an i^(th) element in e_(i) is 1, all other elements are 0, andiε{1, 2, 3, 4}; A is a constant.

In this embodiment, optionally, when the rank is determined to be 1, theprecoding matrices W included in the codebook set are determinedaccording to Table A:

TABLE A i₂ i₁ 0 1 2 3 0-15 W_(i) ₁ _(,0) ⁽¹⁾ W_(i) ₁ _(,1) ⁽¹⁾ W_(i) ₁_(,2) ⁽¹⁾ W_(i) ₁ _(,3) ⁽¹⁾ i₂ i₁ 4 5 6 7 0-15 W_(i) ₁ _(+8,0) ⁽¹⁾ W_(i)₁ _(+8,1) ⁽¹⁾ W_(i) ₁ _(+8,2) ⁽¹⁾ W_(i) ₁ _(+8,3) ⁽¹⁾ i₂ i₁ 8 9 10 110-15 W_(i) ₁ _(+16,0) ⁽¹⁾ W_(i) ₁ _(+16,1) ⁽¹⁾ W_(i) ₁ _(+16,2) ⁽¹⁾W_(i) ₁ _(+16,3) ⁽¹⁾ i₂ i₁ 12 13 14 15 0-15 W_(i) ₁ _(+24,0) ⁽¹⁾ W_(i) ₁_(+24,1) ⁽¹⁾ W_(i) ₁ _(+24,2) ⁽¹⁾ W_(i) ₁ _(+24,3) ⁽¹⁾

where

${W_{m,k}^{(1)} = {\frac{1}{2}\begin{bmatrix}v_{m} \\{\varphi_{k}{\gamma(m)}v_{m}}\end{bmatrix}}},{{\gamma(m)} = e^{j\; 2\pi\frac{{({m - i_{1}})}/4}{32}}},{v_{m} = \begin{bmatrix}1 & e^{j\; 2\pi\;{m/32}}\end{bmatrix}},$φ_(k)=e^(jπk/2), and m and k are nonnegative integers; i₁ represents thefirst codebook index; i₂ represents the second codebook index.

In this embodiment, optionally, when the rank determined by the UE is 2,W₂ satisfies the following equation:

$W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ {\left( {e_{1},e_{1}} \right),\left( {e_{2},e_{2}} \right),\left( {e_{3},e_{3}} \right),\left( {e_{4},e_{4}} \right),\left( {e_{1},e_{2}} \right),\left( {e_{2},e_{3}} \right),\left( {e_{1},e_{4}} \right),\left( {e_{2},e_{4}} \right)} \right\}$

where e_(i) represents a column vector with a dimension of 4×1, ani^(th) element in e_(i) is 1, all other elements are 0, and iε{1, 2, 3,4}; B is a constant.

In this embodiment, optionally, when the rank is determined to be 2, W₂satisfies the following equation:

$W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & Y_{2}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{- Y_{1}} & Y_{2}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{- Y_{1}} & {- Y_{2}}\end{bmatrix}}} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ \left( {e_{2},e_{4}} \right) \right\}$$W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ {\left( {e_{1},e_{1}} \right),\left( {e_{2},e_{2}} \right),\left( {e_{3},e_{3}} \right),\left( {e_{4},e_{4}} \right)} \right\}$$W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{2} & {- Y_{1}}\end{bmatrix}},} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ {\left( {e_{1},e_{3}} \right),\left( {e_{2},e_{4}} \right),\left( {e_{3},e_{1}} \right),\left( {e_{4},e_{2}} \right)} \right\}$

where e_(i) represents a column vector with a dimension of 4×1, ani^(th) element in e_(i) is 1, all other elements are 0, and iε{1, 2, 3,4}; B is a constant.

In this embodiment, optionally, when the rank determined by the UE is 2,the precoding matrices W included in the codebook set are determinedaccording to Table B1 or B2:

TABLE B1 i₂ i₁ 0 1 2 3 0-15 W_(i) ₁ _(,i) ₁ _(,0) ⁽²⁾ W_(i) ₁ _(,i) ₁_(,1) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+8,0) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+8,1) ⁽²⁾ i₂i₁ 4 5 6 7 0-15 W_(i) ₁ _(+16,i) ₁ _(+16,0) ⁽²⁾ W_(i) ₁ _(+16,i) ₁_(+16,1) ⁽²⁾ W_(i) ₁ _(+24,i) ₁ _(+24,0) ⁽²⁾ W_(i) ₁ _(+24,i) ₁ _(+24,1)⁽²⁾ i₂ i₁ 8 9 10 11 0-15 W_(i) ₁ _(,i) ₁ _(+8,0) ⁽²⁾ W_(i) ₁ _(,i) ₁_(+8,1) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+16,0) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+16,1)⁽²⁾ i₂ i₁ 12 13 14 15 0-15 W_(i) ₁ _(,i) ₁ _(+24,0) ⁽²⁾ W_(i) ₁ _(,i) ₁_(+24,1) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+24,0) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+24,1)⁽²⁾

TABLE B2 i₂ i₁ 0 1 2 3 0-15 W_(i) ₁ _(,i) ₁ _(,0) ⁽²⁾ W_(i) ₁ _(,i) ₁_(,1) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+8,0) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+8,1) ⁽²⁾ i₂i₁ 4 5 6 7 0-15 W_(i) ₁ _(+16,i) ₁ _(+16,0) ⁽²⁾ W_(i) ₁ _(+16,i) ₁_(+16,1) ⁽²⁾ W_(i) ₁ _(+24,i) ₁ _(+24,0) ⁽²⁾ W_(i) ₁ _(+24,i) ₁ _(+24,1)⁽²⁾ i₂ i₁ 8 9 10 11 0-15 {tilde over (W)}_(i) ₁ _(+8,i) ₁ _(+24,0) ⁽²⁾W_(i) ₁ _(+8,i) ₁ _(+24,0) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+24,2) ⁽²⁾ {tildeover (W)}_(i) ₁ _(+8,i) ₁ _(+24,2) ⁽²⁾ i₂ i₁ 12 13 14 15 0-15

where

${W_{m,m^{\prime},k}^{(2)} = {\frac{1}{\sqrt{8}}\begin{bmatrix}v_{m} & v_{m^{\prime}} \\{\varphi_{k}v_{m}} & {{- \varphi_{k}}v_{m^{\prime}}}\end{bmatrix}}},{{\overset{\sim}{W}}_{m,m^{\prime},k}^{(2)} = {\frac{1}{\sqrt{8}}\begin{bmatrix}v_{m} & v_{m^{\prime}} \\{\varphi_{k}v_{m}} & {\varphi_{k}v_{m^{\prime}}}\end{bmatrix}}},{{\overset{\overset{\sim}{\sim}}{W}}_{m,m^{\prime},k}^{(2)} = {\frac{1}{\sqrt{8}}\begin{bmatrix}v_{m} & v_{m^{\prime}} \\{\varphi_{k}v_{m^{\prime}}} & {{- \varphi_{k}}v_{m}}\end{bmatrix}}},{v_{m} = \begin{bmatrix}1 & e^{j\; 2\pi\;{m/32}}\end{bmatrix}},{v_{m^{\prime}} = \begin{bmatrix}1 & e^{j\; 2\pi\;{m^{\prime}/32}}\end{bmatrix}},$φ_(k)=e^(jπk/2), and m, m′, and k are nonnegative integers; i₁represents the first codebook index; i₂ represents the second codebookindex.

In this embodiment, optionally, when the received rank is 2, the valuerange of n may be the set {0, 1, 2, 3, 4, 5, 6, 7} or {8, 9, 10, 11, 12,13, 14, 15}.

In this embodiment, optionally, a precoding matrix set corresponding tothe first codebook index corresponding to the first PMI includesprecoding matrices U1 and U2, where the precoding matrices U1 and U2 areindicated by the second codebook index, where:

${{U\; 1} = {\frac{1}{A}\begin{bmatrix}v \\{\beta\; v}\end{bmatrix}}},{{U\; 2} = {\frac{1}{A}\begin{bmatrix}v \\{{- \beta}\; v}\end{bmatrix}}},{v = \begin{bmatrix}1 \\q_{1}^{n + {({8n\mspace{14mu}{mod}\mspace{14mu} 32})}}\end{bmatrix}},$β=j^(└n/4┘)*α(i), i=(n mod 4)+1, α(i)=q₁ ^(2(i-1)), and A is a constant.

It should be understood that in this embodiment, “mod” represents amodulo operation.

Therefore, by means of the method for transmitting a 4-antenna precodingmatrix according to this embodiment, more precoding matrices that areapplicable to a uniform linear array antenna may be indicated withoutchanging a feedback mode or feedback bits, and it may also be ensuredthat performance for application of a dual-polarized antenna is notaffected, so that system performance may be improved and user experiencemay be enhanced.

In this embodiment, optionally, a value range of the first codebookindex corresponding to the first PMI and a value range of the secondcodebook index corresponding to the second PMI have an associationrelationship. Optionally, that a value range of the first codebook indexcorresponding to the first PMI and a value range of the second codebookindex corresponding to the second PMI have an association relationshipincludes the value range of the second codebook index corresponding tothe second PMI is uniquely determined according to a value and/or thevalue range of the first codebook index corresponding to the first PMI.

In this embodiment, optionally, that a value range of the first codebookindex corresponding to the first PMI and a value range of the secondcodebook index corresponding to the second PMI have an associationrelationship includes the value range of the first codebook indexcorresponding to the first PMI includes at least two first value setshaving different elements, the value range of the second codebook indexcorresponding to the second PMI includes at least two second value setshaving different elements, and the at least two first value sets and theat least two second value sets having a one-to-one correspondence.

It should be understood that the number of the first value sets is equalto the number of the second value sets. It should be further understoodthat the elements in the first value sets are different from each other,and the elements in the second value sets are also different from eachother.

Optionally, each first value set of the at least two first value setsincludes at least two values, and each second value set of the at leasttwo second value sets includes at least two values.

In this embodiment, the value range of the first codebook indexcorresponding to the first PMI and the value range of the secondcodebook index corresponding to the second PMI have an associationrelationship; therefore, by means of the method for transmitting aprecoding matrix according to this embodiment, more precoding matricesthat are applicable to a uniform linear array antenna may be indicatedwithout changing a feedback mode or feedback bits, and it may also beensured that performance for application of a dual-polarized antenna isnot affected, so that system performance may be improved and userexperience may be enhanced.

In this embodiment, optionally, when the rank is determined to be 1, thefirst PMI, the second PMI, the first codebook index corresponding to thefirst PMI, and the second codebook index corresponding to the second PMIare determined according to Table C1, C2, C3, or C4:

TABLE C1 I_(PMI1) i₁ = I_(PMI1) I_(PMI2) i₂ 0 0 0 0 0 0 1 2 1 1 0 4 1 11 6 2 2 0 8 2 2 1 10 3 3 0 12 3 3 1 14 4 4 0 1 4 4 1 3 5 5 0 5 5 5 1 7 66 0 9 6 6 1 11 7 7 0 13 7 7 1 15

TABLE C2 I_(PMI1) i₁ = I_(PMI1) + 8 I_(PMI2) i₂ 0 8 0 0 0 8 1 2 1 9 0 41 9 1 6 2 10 0 8 2 10 1 10 3 11 0 12 3 11 1 14 4 12 0 1 4 12 1 3 5 13 05 5 13 1 7 6 14 0 9 6 14 1 11 7 15 0 13 7 15 1 15

TABLE C3 I_(PMI1) i₁ = 2I_(PMI1) I_(PMI2) i₂ 0 0 0 0 0 0 1 2 1 2 0 8 1 21 10 2 4 0 1 2 4 1 3 3 6 0 9 3 6 1 11 4 8 0 0 4 8 1 2 5 10 0 8 5 10 1 106 12 0 1 6 12 1 3 7 14 0 9 7 14 1 11

TABLE C4 I_(PMI1) i₁ = 2I_(PMI1) + 1 I_(PMI2) i₂ 0 1 0 4 0 1 1 6 1 3 012 1 3 1 14 2 5 0 5 2 5 1 7 3 7 0 13 3 7 1 15 4 9 0 4 4 9 1 6 5 11 0 125 11 1 14 6 13 0 5 6 13 1 7 7 15 0 13 7 15 1 15

where I_(PMI1) represents the first PMI, I_(PMI2) represents the secondPMI, i₁ represents the first codebook index, and i₂ represents thesecond codebook index.

It should be understood that interaction and related features andfunctions of the base station and the user equipment that are describedon the base station side correspond to the description on the userequipment side with reference to FIG. 1, which are not described hereinany further for brevity.

It should be further understood that sequence numbers of the foregoingprocesses do not mean execution sequences in various embodiments. Theexecution sequences of the processes should be determined according tofunctions and internal logic of the processes, and should not beconstrued as any limitation on the implementation processes of theembodiments.

Therefore, in the method for transmitting a 4-antenna precoding matrixaccording to this embodiment, the value range of the first codebookindex corresponding to the first PMI and the value range of the secondcodebook index corresponding to the second PMI have an associationrelationship, so that more precoding matrices that are applicable to auniform linear array antenna may be indicated during codebooksubsampling without changing a feedback mode or feedback bits, and eachprecoding matrix in a codebook set after the subsampling is applicableto a dual-polarized antenna, which may ensure that performance forapplication of the dual-polarized antenna is not affected, improvesystem performance and enhance user experience.

FIG. 5 shows a schematic flowchart of a method 70 for transmitting a4-antenna precoding matrix according to an embodiment. The method 70 maybe performed, for example, by a base station. As shown in FIG. 5, themethod 70 includes the following steps.

S71: Receive a jointly coded value sent by a user equipment.

S72: Determine a value of a first codebook index and a rank used forindicating the number of transmission layers according to the jointlycoded value, a correspondence between the jointly coded value and therank and a correspondence between the jointly coded value and the firstcodebook index.

The value of the first codebook index corresponds to one precodingmatrix set in a codebook set, the codebook set corresponds to the rank,precoding matrices included in the codebook set are represented by thefirst codebook index and a second codebook index, and the precodingmatrices W included in the codebook set satisfy the following equation:

W=W₁×W₂, where

${W_{1} = \begin{bmatrix}X_{n} & 0 \\0 & X_{n}\end{bmatrix}},{X_{n} = \begin{bmatrix}1 & 1 & 1 & 1 \\q_{1}^{n} & q_{1}^{n + 8} & q_{1}^{n + 16} & q_{1}^{n + 24}\end{bmatrix}},$q₁=e^(j2π/32), and n=0, 1, . . . , 15; and

the first codebook index corresponds to one value of n, and a valuerange of n is a set {0, 1, 2, 3, 4, 5, 6, 7}, {8, 9, 10, 11, 12, 13, 14,15}, {0, 2, 4, 6}, {1, 3, 5, 7}, {8, 10, 12, 14}, or {9, 11, 13, 15}.

Therefore, the method for transmitting a 4-antenna precoding matrixaccording to this embodiment may prevent a problem where precodingmatrices are repeated after subsampling, thereby improving systemperformance and enhancing user experience.

In this embodiment, optionally, when the rank is determined to be 1, W₂satisfies the following equation:

${W_{2} \in \left\{ {{\frac{1}{A}\begin{bmatrix}Y \\{{\alpha(i)}Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{j\;{\alpha(i)}Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{{- {\alpha(i)}}Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{{- j}\;{\alpha(i)}Y}\end{bmatrix}}} \right\}},$

where Yε{e₁,e₂,e₃,e₄}, α(i)=q₁ ^(2(i-1)); when Y is α(i) is α(1); when Yis e₂, α(i) is α(2); when Y is e₃, α(i) is α(3); when Y is e₄, α(i) isα(4); e_(i) represents a column vector with a dimension of 4×1, where ani^(th) element in e_(i) is 1, all other elements are 0, and iε{1, 2, 3,4}; A is a constant.

In this embodiment, optionally, when the rank is determined to be 2, W₂satisfies the following equation:

${W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ {\left( {e_{1},e_{1}} \right),\left( {e_{2},e_{2}} \right),\left( {e_{3},e_{3}} \right),\left( {e_{4},e_{4}} \right),\left( {e_{1},e_{2}} \right),\left( {e_{2},e_{3}} \right),\left( {e_{1},e_{4}} \right),\left( {e_{2},e_{4}} \right)} \right\}};{or}$$W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & Y_{2}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{- Y_{1}} & Y_{2}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{- Y_{1}} & {- Y_{2}}\end{bmatrix}}} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ \left( {e_{2},e_{4}} \right) \right\}$$W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ {\left( {e_{1},e_{1}} \right),\left( {e_{2},e_{2}} \right),\left( {e_{3},e_{3}} \right),\left( {e_{4},e_{4}} \right)} \right\}$$W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{2} & {- Y_{1}}\end{bmatrix}},} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ {\left( {e_{1},e_{3}} \right),\left( {e_{2},e_{4}} \right),\left( {e_{3},e_{1}} \right),\left( {e_{4},e_{2}} \right)} \right\}$

where e_(i) represents a column vector with a dimension of 4×1, ani^(th) element in e_(i) is 1, all other elements are 0, and iε{1, 2, 3,4}; B is a constant.

In this embodiment, optionally, when the number of bits bearing thejointly coded value is 4, the correspondence between the jointly codedvalue and the rank and the correspondence between the jointly codedvalue and the first codebook index are determined according to thefollowing Table D:

TABLE D I_(RI/PMI1) RI i₁ 0-7 1 I_(RI/PMI1)  8-15 2 I_(RI/PMI1) − 8

where I_(RI/PMI1) represents the jointly coded value, RI represents therank, and i₁ represents the first codebook index.

In this embodiment, optionally, when the number of bits bearing thejointly coded value is 3, the correspondence between the jointly codedvalue and the rank and the correspondence between the jointly codedvalue and the first codebook index are determined according to thefollowing Table E:

TABLE E I_(RI/PMI1) RI i₁ 0-3 1 2 × I_(RI/PMI1) 4-7 2 2 × (I_(RI/PMI1) −4)

where I_(RI/PMI1) represents the jointly coded value, RI represents therank, and i₁ represents the first codebook index.

It should be understood that in this embodiment, when the rank isdetermined to be 1, the precoding matrices W included in the codebookset are determined according to Table A:

TABLE A i₂ i₁ 0 1 2 3 0-15 W_(i) ₁ _(,0) ⁽¹⁾ W_(i) ₁ _(,1) ⁽¹⁾ W_(i) ₁_(,2) ⁽¹⁾ W_(i) ₁ _(,3) ⁽¹⁾ i₂ i₁ 4 5 6 7 0-15 W_(i) ₁ _(+8,0) ⁽¹⁾ W_(i)₁ _(+8,1) ⁽¹⁾ W_(i) ₁ _(+8,2) ⁽¹⁾ W_(i) ₁ _(+8,3) ⁽¹⁾ i₂ i₁ 8 9 10 110-15 W_(i) ₁ _(+16,0) ⁽¹⁾ W_(i) ₁ _(+16,1) ⁽¹⁾ W_(i) ₁ _(+16,2) ⁽¹⁾W_(i) ₁ _(+16,3) ⁽¹⁾ i₂ i₁ 12 13 14 15 0-15 W_(i) ₁ _(+24,0) ⁽¹⁾ W_(i) ₁_(+24,1) ⁽¹⁾ W_(i) ₁ _(+24,2) ⁽¹⁾ W_(i) ₁ _(+24,3) ⁽¹⁾

where

${W_{m,k}^{(1)} = {\frac{1}{2}\begin{bmatrix}v_{m} \\{\varphi_{k}{\gamma(m)}v_{m}}\end{bmatrix}}},{{\gamma(m)} = e^{j\; 2\pi\frac{{({m - i_{1}})}/4}{32}}},{v_{m} = \begin{bmatrix}1 & e^{j\; 2\pi\;{m/32}}\end{bmatrix}},$φ_(k)=e^(jπk/2), and m and k are nonnegative integers; i₁ represents thefirst codebook index; i₂ represents the second codebook index.

It should be further understood that in this embodiment, when the rankdetermined by the UE is 2, the precoding matrices W included in thecodebook set are determined according to Table B1 or B2:

TABLE B1 i₂ i₁ 0 1 2 3 0-15 W_(i) ₁ _(,i) ₁ _(,0) ⁽²⁾ W_(i) ₁ _(,i) ₁_(,1) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+8,0) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+8,1) ⁽²⁾ i₂i₁ 4 5 6 7 0-15 W_(i) ₁ _(+16,i) ₁ _(+16,0) ⁽²⁾ W_(i) ₁ _(+16,i) ₁_(+16,1) ⁽²⁾ W_(i) ₁ _(+24,i) ₁ _(+24,0) ⁽²⁾ W_(i) ₁ _(+24,i) ₁ _(+24,1)⁽²⁾ i₂ i₁ 8 9 10 11 0-15 W_(i) ₁ _(,i) ₁ _(+8,0) ⁽²⁾ W_(i) ₁ _(,i) ₁_(+8,1) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+16,0) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+16,1)⁽²⁾ i₂ i₁ 12 13 14 15 0-15 W_(i) ₁ _(,i) ₁ _(+24,0) ⁽²⁾ W_(i) ₁ _(,i) ₁_(+24,1) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+24,0) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+24,1)⁽²⁾

TABLE B2 i₂ i₁ 0 1 2 3 0-15 W_(i) ₁ _(,i) ₁ _(,0) ⁽²⁾ W_(i) ₁ _(,i) ₁_(,1) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+8,0) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+8,1) ⁽²⁾ i₂i₁ 4 5 6 7 0-15 W_(i) ₁ _(+16,i) ₁ _(+16,0) ⁽²⁾ W_(i) ₁ _(+16,i) ₁_(+16,1) ⁽²⁾ W_(i) ₁ _(+24,i) ₁ _(+24,0) ⁽²⁾ W_(i) ₁ _(+24,i) ₁ _(+24,1)⁽²⁾ i₂ i₁ 8 9 10 11 0-15 {tilde over (W)}_(i) ₁ _(+8,i) ₁ _(+24,0) ⁽²⁾W_(i) ₁ _(+8,i) ₁ _(+24,0) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+24,2) ⁽²⁾ {tildeover (W)}_(i) ₁ _(+8,i) ₁ _(+24,2) ⁽²⁾ i₂ i₁ 12 13 14 15 0-15

where

${W_{m,m^{\prime},k}^{(2)} = {\frac{1}{\sqrt{8}}\begin{bmatrix}v_{m} & v_{m^{\prime}} \\{\varphi_{k}v_{m}} & {{- \varphi_{k}}v_{m^{\prime}}}\end{bmatrix}}},{{\overset{\sim}{W}}_{m,m^{\prime},k}^{(2)} = {\frac{1}{\sqrt{8}}\begin{bmatrix}v_{m} & v_{m^{\prime}} \\{\varphi_{k}v_{m}} & {\varphi_{k}v_{m^{\prime}}}\end{bmatrix}}},{{\overset{\overset{\sim}{\sim}}{W}}_{m,m^{\prime},k}^{(2)} = {\frac{1}{\sqrt{8}}\begin{bmatrix}v_{m} & v_{m^{\prime}} \\{\varphi_{k}v_{m^{\prime}}} & {{- \varphi_{k}}v_{m}}\end{bmatrix}}},{v_{m} = \begin{bmatrix}1 & e^{j\; 2\pi\;{m/32}}\end{bmatrix}},{v_{m^{\prime}} = \begin{bmatrix}1 & e^{j\; 2\pi\;{m^{\prime}/32}}\end{bmatrix}},$φ_(k)=e^(jπk/2), and m, m′, and k are nonnegative integers; i₁represents the first codebook index; i₂ represents the second codebookindex.

It should be understood that in this embodiment, the jointly coded valuerepresents a value generated by performing joint coding on the rank anda first PMI, which is not described herein any further for brevity.

It should be understood that interaction and related features andfunctions of the base station and the user equipment that are describedon the base station side correspond to the description on the userequipment side with reference to FIG. 2, which are not described hereinany further for brevity.

It should be further understood that sequence numbers of the foregoingprocesses do not mean execution sequences in various embodiments. Theexecution sequences of the processes should be determined according tofunctions and internal logic of the processes, and should not beconstrued as any limitation on the implementation processes of theembodiments.

Therefore, the method for transmitting a 4-antenna precoding matrixaccording to this embodiment of the present invention may prevent aproblem where precoding matrices are repeated after subsampling, therebyimproving system performance and enhancing user experience.

FIG. 6 shows a schematic flowchart of a method 80 for transmitting a4-antenna precoding matrix according to an embodiment. The method 80 maybe performed, for example, by a base station. As shown in FIG. 6, themethod 80 includes the following steps.

S81: Receive a second precoding matrix indicator PMI, a first codebookindex, and a rank used for indicating the number of transmission layersthat are sent by a user equipment.

S82: Determine a first precoding matrix in a codebook set correspondingto the rank according to the second PMI and the first codebook index,where precoding matrices included in the codebook set are represented bythe first codebook index and a second codebook index, the second PMI andthe second codebook index have a first correspondence, and for one givenfirst codebook index, a value range of the second codebook indexcorresponding to a value range of the second PMI is a proper subset of avalue range of the second codebook index.

The precoding matrices W included in the codebook set satisfy thefollowing equation:

W=W₁×W₂, where

${W_{1} = \begin{bmatrix}X_{n} & 0 \\0 & X_{n}\end{bmatrix}},{X_{n} = \begin{bmatrix}1 & 1 & 1 & 1 \\q_{1}^{n} & q_{1}^{n + 8} & q_{1}^{n + 16} & q_{1}^{n + 24}\end{bmatrix}},$q₁=e^(j2π/32), and n=0, 1, . . . , 15;

the first codebook index corresponds to one value of n, and a valuerange of n is a set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15};and

when the received rank is 2, in precoding matrix sets that aredetermined according to the first codebook index and the second codebookindex corresponding to the value range of the second PMI, a firstprecoding matrix set corresponding to a first codebook index i_(1,a) anda second precoding matrix set corresponding to a first codebook indexi_(1,a+8) are mutually exclusive, where the first codebook index i_(1,a)represents a first codebook index corresponding to n whose value is a,the first codebook index i_(1,a+8) represents a first codebook indexcorresponding to n whose value is a+8, and a ε{0, 1, 2, 3, 4, 5, 6, 7}.

Therefore, the method for transmitting a 4-antenna precoding matrixaccording to this embodiment may prevent a problem where precodingmatrices are repeated after subsampling, thereby improving systemperformance and enhancing user experience.

In this embodiment, optionally, a value range of the first codebookindex i₁ is 0≦i₁≦15, and a value range of the second codebook index i₂is 0≦i₂≦L₂−1, where L₂ is a positive integer. For example, a value rangeof L₂ is 1≦L₂≦16, that is, the value range of the second codebook indexi₂ is, for example, 0≦i₂≦15.

In this embodiment, optionally, when the received rank is 1, W₂satisfies the following equation:

${W_{2} \in \left\{ {{\frac{1}{A}\begin{bmatrix}Y \\{{\alpha(i)}Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{j\;{\alpha(i)}Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{{- {\alpha(i)}}Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{{- j}\;{\alpha(i)}Y}\end{bmatrix}}} \right\}},$

where Yε{e₁,e₂,e₃,e₄}, α(i)=q₁ ^(2(i-1)); when Y is e₁, α(i) is α(1);when Y is e₂, α(i) is α(2); when Y is e₃, α(i) is α(3); when Y is e₄,α(i) is α(4); e_(i) represents a column vector with a dimension of 4×1,where an i^(th) element in e_(i) is 1, all other elements are 0, andiε{1, 2, 3, 4}; A is a constant.

In this embodiment, optionally, when the received rank is 2, W₂satisfies the following equation:

$\mspace{20mu}{W_{2} \in \left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}} \right\}}$(Y₁, Y₂) ∈ {(e₁, e₁), (e₂, e₂), (e₃, e₃), (e₄, e₄), (e₁, e₂), (e₂, e₃), (e₁, e₄), (e₂, e₄)};  or$W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & Y_{2}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{- Y_{1}} & Y_{2}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{- Y_{1}} & {- Y_{2}}\end{bmatrix}}} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ \left( {e_{2},e_{4}} \right) \right\}$$W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ {\left( {e_{1},e_{1}} \right),\left( {e_{2},e_{2}} \right),\left( {e_{3},e_{3}} \right),\left( {e_{4},e_{4}} \right)} \right\}$$W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{2} & {- Y_{1}}\end{bmatrix}},} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ {\left( {e_{1},e_{3}} \right),\left( {e_{2},e_{4}} \right),\left( {e_{3},e_{1}} \right),\left( {e_{4},e_{2}} \right)} \right\}$

where e_(i) represents a column vector with a dimension of 4×1, ani^(th) element in e_(i) is 1, all other elements are 0, and iε{1, 2, 3,4}; B is a constant.

In this embodiment, optionally, when the received rank is 2, mutualrelationships between the second PMI, the first codebook index, and thesecond codebook index are determined according to Table F1 or F2:

TABLE F1 I_(PMI2) i₁ i₂ 0-3 0-7 2 × I_(PMI2)  8-15 2 × I_(PMI2) + 1

TABLE F2 I_(PMI2) i₁ i₂ 0-3 0-7 2 × I_(PMI2)  8-15 2 × I_(PMI2) + 8

where I_(PMI2) represents the second PMI, i₁ represents the firstcodebook index, and i₂ represents the second codebook index.

It should be understood that in this embodiment, when the rank isdetermined to be 1, the precoding matrices W included in the codebookset are determined according to Table A:

TABLE A i₂ i₁ 0 1 2 3 0-15 W_(i) ₁ _(,0) ⁽¹⁾ W_(i) ₁ _(,1) ⁽¹⁾ W_(i) ₁_(,2) ⁽¹⁾ W_(i) ₁ _(,3) ⁽¹⁾ i₂ i₁ 4 5 6 7 0-15 W_(i) ₁ _(+8,0) ⁽¹⁾ W_(i)₁ _(+8,1) ⁽¹⁾ W_(i) ₁ _(+8,2) ⁽¹⁾ W_(i) ₁ _(+8,3) ⁽¹⁾ i₂ i₁ 8 9 10 110-15 W_(i) ₁ _(+16,0) ⁽¹⁾ W_(i) ₁ _(+16,1) ⁽¹⁾ W_(i) ₁ _(+16,2) ⁽¹⁾W_(i) ₁ _(+16,3) ⁽¹⁾ i₂ i₁ 12 13 14 15 0-15 W_(i) ₁ _(+24,0) ⁽¹⁾ W_(i) ₁_(+24,1) ⁽¹⁾ W_(i) ₁ _(+24,2) ⁽¹⁾ W_(i) ₁ _(+24,3) ⁽¹⁾

where

${W_{m,k}^{(1)} = {\frac{1}{2}\begin{bmatrix}v_{m} \\{\varphi_{k}{\gamma(m)}v_{m}}\end{bmatrix}}},{{\gamma(m)} = e^{j\; 2\pi\frac{{({m - i_{1}})}/4}{32}}},{v_{m} = \begin{bmatrix}1 & e^{j\; 2\pi\;{m/32}}\end{bmatrix}},$φ_(k)=e^(jπk/2), and m and k are nonnegative integers; i₁ represents thefirst codebook index; i₂ represents the second codebook index.

It should be further understood that in this embodiment, when the rankdetermined by the UE is 2, the precoding matrices W included in thecodebook set are determined according to Table B1 or B2:

TABLE B1 i₂ i₁ 0 1 2 3 0-15 W_(i) ₁ _(,i) ₁ _(,0) ⁽²⁾ W_(i) ₁ _(,i) ₁_(,1) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+8,0) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+8,1) ⁽²⁾ i₂i₁ 4 5 6 7 0-15 W_(i) ₁ _(+16,i) ₁ _(+16,0) ⁽²⁾ W_(i) ₁ _(+16,i) ₁_(+16,1) ⁽²⁾ W_(i) ₁ _(+24,i) ₁ _(+24,0) ⁽²⁾ W_(i) ₁ _(+24,i) ₁ _(+24,1)⁽²⁾ i₂ i₁ 8 9 10 11 0-15 W_(i) ₁ _(,i) ₁ _(+8,0) ⁽²⁾ W_(i) ₁ _(,i) ₁_(+8,1) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+16,0) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+16,1)⁽²⁾ i₂ i₁ 12 13 14 15 0-15 W_(i) ₁ _(,i) ₁ _(+24,0) ⁽²⁾ W_(i) ₁ _(,i) ₁_(+24,1) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+24,0) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+24,1)⁽²⁾

TABLE B2 i₂ i₁ 0 1 2 3 0-15 W_(i) ₁ _(,i) ₁ _(,0) ⁽²⁾ W_(i) ₁ _(,i) ₁_(,1) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+8,0) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+8,1) ⁽²⁾ i₂i₁ 4 5 6 7 0-15 W_(i) ₁ _(+16,i) ₁ _(+16,0) ⁽²⁾ W_(i) ₁ _(+16,i) ₁_(+16,1) ⁽²⁾ W_(i) ₁ _(+24,i) ₁ _(+24,0) ⁽²⁾ W_(i) ₁ _(+24,i) ₁ _(+24,1)⁽²⁾ i₂ i₁ 8 9 10 11 0-15 {tilde over (W)}_(i) ₁ _(+8,i) ₁ _(+24,0) ⁽²⁾W_(i) ₁ _(+8,i) ₁ _(+24,0) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+24,2) ⁽²⁾ {tildeover (W)}_(i) ₁ _(+8,i) ₁ _(+24,2) ⁽²⁾ i₂ i₁ 12 13 14 15 0-15

where

${W_{m,m^{\prime},k}^{(2)} = {\frac{1}{\sqrt{8}}\begin{bmatrix}v_{m} & v_{m^{\prime}} \\{\varphi_{k}v_{m}} & {{- \varphi_{k}}v_{m^{\prime}}}\end{bmatrix}}},{{\overset{\sim}{W}}_{m,m^{\prime},k}^{(2)} = {\frac{1}{\sqrt{8}}\begin{bmatrix}v_{m} & v_{m^{\prime}} \\{\varphi_{k}v_{m}} & {\varphi_{k}v_{m^{\prime}}}\end{bmatrix}}},{{\overset{\overset{\sim}{\sim}}{W}}_{m,m^{\prime},k}^{(2)} = {\frac{1}{\sqrt{8}}\begin{bmatrix}v_{m} & v_{m^{\prime}} \\{\varphi_{k}v_{m^{\prime}}} & {{- \varphi_{k}}v_{m^{\prime}}}\end{bmatrix}}},{v_{m} = \begin{bmatrix}1 & e^{j\; 2\pi\;{m/32}}\end{bmatrix}},{v_{m^{\prime}} = \begin{bmatrix}1 & e^{j\; 2\pi\;{m^{\prime}/32}}\end{bmatrix}},$φ_(k)=e^(jπk/2), and m, m′, and k are nonnegative integers; i₁represents the first codebook index; i₂ represents the second codebookindex.

In this embodiment, optionally, when the received rank is 3 or 4, theprecoding matrices included in the codebook set corresponding to therank are:

four precoding matrices with codebook indexes 0 to 3 in Table G; or

four precoding matrices with codebook indexes 4 to 7 in Table G; or

four precoding matrices with codebook indexes 12 to 15 in Table G,

TABLE G Codebook RI Index u_(n) 1 2 3 4 0 u₀ = [1 −1 −1 −1]^(T) W₀^({1}) W₀ ^({14})/{square root over (2)} W₀ ^({124})/{square root over(3)} W₀ ^({1234})/2 1 u₁ = [1 −j 1 j]^(T) W₁ ^({1}) W₁ ^({12})/{squareroot over (2)} W₁ ^({123})/{square root over (3)} W₁ ^({1234})/2 2 u₂ =[1 1 −1 1]^(T) W₂ ^({1}) W₂ ^({12})/{square root over (2)} W₂^({123})/{square root over (3)} W₂ ^({3214})/2 3 u₃ = [1 j 1 −j]^(T) W₃^({1}) W₃ ^({12})/{square root over (2)} W₃ ^({123})/{square root over(3)} W₃ ^({3214})/2 4 u₄ = [1 (−1 − j)/{square root over (2)} −j (1 −j)/{square root over (2)}]^(T) W₄ ^({1}) W₄ ^({14})/{square root over(2)} W₄ ^({124})/{square root over (3)} W₄ ^({1234})/2 5 u₅ = [1 (1 −j)/{square root over (2)} j (−1 − j)/{square root over (2)}]^(T) W₅^({1}) W₅ ^({14})/{square root over (2)} W₅ ^({124})/{square root over(3)} W₅ ^({1234})/2 6 u₆ = [1 (1 + j)/{square root over (2)} −j (−1 +j)/{square root over (2)}]^(T) W₆ ^({1}) W₆ ^({13})/{square root over(2)} W₆ ^({134})/{square root over (3)} W₆ ^({1324})/2 7 u₇ = [1 (−1 +j)/{square root over (2)} j (1 + j)/{square root over (2)}]^(T) W₇^({1}) W₇ ^({13})/{square root over (2)} W₇ ^({134})/{square root over(3)} W₇ ^({1324})/2 8 u₈ = [1 −1 1 1]^(T) W₈ ^({1}) W₈ ^({12})/{squareroot over (2)} W₈ ^({124})/{square root over (3)} W₈ ^({1234})/2 9 u₉ =[1 −j −1 −j]^(T) W₉ ^({1}) W₉ ^({14})/{square root over (2)} W₉^({134})/{square root over (3)} W₉ ^({1234})/2 10 u₁₀ = [1 1 1 −1]^(T)W₁₀ ^({1}) W₁₀ ^({13})/{square root over (2)} W₁₀ ^({123})/{square rootover (3)} W₁₀ ^({1324})/2 11 u₁₁ = [1 j −1 j]^(T) W₁₁ ^({1}) W₁₁^({13})/{square root over (2)} W₁₁ ^({134})/{square root over (3)} W₁₁^({1324})/2 12 u₁₂ = [1 −1 −1 1]^(T) W₁₂ ^({1}) W₁₂ ^({12})/{square rootover (2)} W₁₂ ^({123})/{square root over (3)} W₁₂ ^({1234})/2 13 u₁₃ =[1 −1 1 −1]^(T) W₁₃ ^({1}) W₁₃ ^({13})/{square root over (2)} W₁₃^({123})/{square root over (3)} W₁₃ ^({1324})/2 14 u₁₄ = [1 1 −1 −1]^(T)W₁₄ ^({1}) W₁₄ ^({13})/{square root over (2)} W₁₄ ^({123})/{square rootover (3)} W₁₄ ^({3214})/2 15 u₁₅ = [1 1 1 1]^(T) W₁₅ ^({1}) W₁₅^({12})/{square root over (2)} W₁₅ ^({123})/{square root over (3)} W₁₅^({1234})/2

where W_(n) ^({s}) represents a matrix formed by a column set {s} of amatrix W_(n)=I−2u_(n)u_(n) ^(H)/u_(n) ^(H)u_(n), and I is a 4×4 identitymatrix.

It should be understood that interaction and related features andfunctions of the base station and the user equipment that are describedon the base station side correspond to the description on the userequipment side with reference to FIG. 3, which are not described hereinany further for brevity.

It should be further understood that sequence numbers of the foregoingprocesses do not mean execution sequences in various embodiments of thepresent invention. The execution sequences of the processes should bedetermined according to functions and internal logic of the processes,and should not be construed as any limitation on the implementationprocesses of the embodiments of the present invention.

Therefore, the method for transmitting a 4-antenna precoding matrixaccording to this embodiment may prevent a problem where precodingmatrices are repeated after subsampling, thereby improving systemperformance and enhancing user experience.

The methods for transmitting a 4-antenna precoding matrix according tothe embodiments are described in detail above with reference to FIG. 1to FIG. 6. The following describes a user equipment and a base stationaccording to the embodiments in detail with reference to FIG. 7 to FIG.18.

FIG. 7 shows a schematic block diagram of a user equipment 100 accordingto an embodiment. As shown in FIG. 7, the user equipment 100 includes: adetermining module 110, configured to determine a rank used forindicating the number of transmission layers, further configured todetermine a first precoding matrix in a codebook set corresponding tothe rank, where precoding matrices included in the codebook set arerepresented by a first codebook index and a second codebook index, andfurther configured to determine a first precoding matrix indicator PMIand a second PMI used for indicating the first precoding matrix, wherethe first PMI and the first codebook index have a first correspondence,and the second PMI and the second codebook index have a secondcorrespondence; and a sending module 120, configured to send, to a basestation, the first PMI and the second PMI that are used for indicatingthe first precoding matrix and determined by the determining module 110,where:

the precoding matrices W included in the codebook set satisfy thefollowing equation:

W=W₁×W₂, where

${W_{1} = \begin{bmatrix}X_{n} & 0 \\0 & X_{n}\end{bmatrix}},{X_{n} = \begin{bmatrix}1 & 1 & 1 & 1 \\q_{1}^{n} & q_{1}^{n + 8} & q_{1}^{n + 16} & q_{1}^{n + 24}\end{bmatrix}},$q₁=e^(j2π/32), and n=0, 1, . . . , 15; and

the first codebook index corresponds to one value of n, and a valuerange of n is a set {0, 1, 2, 3, 4, 5, 6, 7}, {8, 9, 10, 11, 12, 13, 14,15}, {0, 2, 4, 6, 8, 10, 12, 14}, or {1, 3, 5, 7, 9, 11, 13, 15}.

Therefore, by means of the user equipment according to this embodiment,more precoding matrices that are applicable to a uniform linear arrayantenna may be indicated without changing a feedback mode or feedbackbits, and it may also be ensured that performance for application of adual-polarized antenna is not affected, so that system performance maybe improved and user experience may be enhanced.

In this embodiment, optionally, a value range of the first codebookindex i₁ is 0≦i₁≦15, and a value range of the second codebook index i₂is 0≦i₂≦L₂−1, where L₂ is a positive integer. For example, a value rangeof L₂ is 1≦L₂≦16, that is, the value range of the second codebook indexi₂ is, for example, 0≦i₂≦15.

In this embodiment, optionally, when the rank determined by thedetermining module 110 is 1, W₂ satisfies the following equation:

${W_{2} \in \left\{ {{\frac{1}{A}\begin{bmatrix}Y \\{{\alpha(i)}Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{j\;{\alpha(i)}Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{{- {\alpha(i)}}Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{{- j}\;{\alpha(i)}Y}\end{bmatrix}}} \right\}},$

where Yε{e₁,e₂,e₃,e₄}, α(i)=q₁ ^(2(i-1)); when Y is e₁, α(i) is α(1);when Y is e₂, α(i) is α(2); when Y is e₃, α(i) is α(3); when Y is e₄,α(i) is α(4); e_(i) represents a column vector with a dimension of 4×1,where an i^(th) element in e_(i) is 1, all other elements are 0, andiε{1, 2, 3, 4}; A is a constant.

In this embodiment, optionally, when the rank determined by thedetermining module 110 is 2, W₂ satisfies the following equation:

$\mspace{20mu}{W_{2} \in \left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}} \right\}}$(Y₁, Y₂) ∈ {(e₁, e₁), (e₂, e₂), (e₃, e₃), (e₄, e₄), (e₁, e₂), (e₂, e₃), (e₁, e₄), (e₂, e₄)};  or$W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & Y_{2}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{- Y_{1}} & Y_{2}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{- Y_{1}} & {- Y_{2}}\end{bmatrix}}} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ \left( {e_{2},e_{4}} \right) \right\}$$W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ {\left( {e_{1},e_{1}} \right),\left( {e_{2},e_{2}} \right),\left( {e_{3},e_{3}} \right),\left( {e_{4},e_{4}} \right)} \right\}$$W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{2} & {- Y_{1}}\end{bmatrix}},} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ {\left( {e_{1},e_{3}} \right),\left( {e_{2},e_{4}} \right),\left( {e_{3},e_{1}} \right),\left( {e_{4},e_{2}} \right)} \right\}$

where e_(i) represents a column vector with a dimension of 4×1, ani^(th) element in e_(i) is 1, all other elements are 0, and iε{1, 2, 3,4}; B is a constant.

In this embodiment, optionally, a precoding matrix set corresponding tothe first codebook index corresponding to the first PMI includesprecoding matrices U1 and U2, where the precoding matrices U1 and U2 areindicated by the second codebook index, where:

${{U\; 1} = {\frac{1}{A}\begin{bmatrix}v \\{\beta\; v}\end{bmatrix}}},{{U\; 2} = {\frac{1}{A}\begin{bmatrix}v \\{{- \beta}\; v}\end{bmatrix}}},{v = \begin{bmatrix}1 \\q_{1}^{n + {({8n\mspace{14mu}{mod}\mspace{14mu} 32})}}\end{bmatrix}},$β=j^(└n/4┘)*α(i), i=(n mod 4)+1, α(i)=q₁ ^(2(i-1)), and A is a constant.

In this embodiment, optionally, when the rank determined by thedetermining module 110 is 1, the precoding matrices W included in thecodebook set are determined according to Table A:

TABLE A i₂ i₁ 0 1 2 3 0-15 W_(i) ₁ _(,0) ⁽¹⁾ W_(i) ₁ _(,1) ⁽¹⁾ W_(i) ₁_(,2) ⁽¹⁾ W_(i) ₁ _(,3) ⁽¹⁾ i₂ i₁ 4 5 6 7 0-15 W_(i) ₁ _(+8,0) ⁽¹⁾ W_(i)₁ _(+8,1) ⁽¹⁾ W_(i) ₁ _(+8,2) ⁽¹⁾ W_(i) ₁ _(+8,3) ⁽¹⁾ i₂ i₁ 8 9 10 110-15 W_(i) ₁ _(+16,0) ⁽¹⁾ W_(i) ₁ _(+16,1) ⁽¹⁾ W_(i) ₁ _(+16,2) ⁽¹⁾W_(i) ₁ _(+16,3) ⁽¹⁾ i₂ i₁ 12 13 14 15 0-15 W_(i) ₁ _(+24,0) ⁽¹⁾ W_(i) ₁_(+24,1) ⁽¹⁾ W_(i) ₁ _(+24,2) ⁽¹⁾ W_(i) ₁ _(+24,3) ⁽¹⁾

where

${W_{m,k}^{(1)} = {\frac{1}{2}\begin{bmatrix}v \\{\varphi_{k}{\gamma(m)}v_{m}}\end{bmatrix}}},{{\gamma(m)} = e^{j\; 2\pi\frac{{({m - i_{1}})}/4}{32}}},{v_{m} = \begin{bmatrix}1 & e^{j\; 2\;\pi\;{m/32}}\end{bmatrix}},$φ_(k)=e^(jπk/2), and m and k are nonnegative integers; i₁ represents thefirst codebook index; i₂ represents the second codebook index.

In this embodiment, optionally, when the rank determined by thedetermining module 110 is 2, the precoding matrices W included in thecodebook set are determined according to Table B1 or B2:

TABLE B1 i₂ i₁ 0 1 2 3 0-15 W_(i) ₁ _(,i) ₁ _(,0) ⁽²⁾ W_(i) ₁ _(,i) ₁_(,1) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+8,0) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+8,1) ⁽²⁾ i₂i₁ 4 5 6 7 0-15 W_(i) ₁ _(+16,i) ₁ _(+16,0) ⁽²⁾ W_(i) ₁ _(+16,i) ₁_(+16,1) ⁽²⁾ W_(i) ₁ _(+24,i) ₁ _(+24,0) ⁽²⁾ W_(i) ₁ _(+24,i) ₁ _(+24,1)⁽²⁾ i₂ i₁ 8 9 10 11 0-15 W_(i) ₁ _(,i) ₁ _(+8,0) ⁽²⁾ W_(i) ₁ _(,i) ₁_(+8,1) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+16,0) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+16,1)⁽²⁾ i₂ i₁ 12 13 14 15 0-15 W_(i) ₁ _(,i) ₁ _(+24,0) ⁽²⁾ W_(i) ₁ _(,i) ₁_(+24,1) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+24,0) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+24,1)⁽²⁾

TABLE B2 i₂ i₁ 0 1 2 3 0-15 W_(i) ₁ _(,i) ₁ _(,0) ⁽²⁾ W_(i) ₁ _(,i) ₁_(,1) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+8,0) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+8,1) ⁽²⁾ i₂i₁ 4 5 6 7 0-15 W_(i) ₁ _(+16,i) ₁ _(+16,0) ⁽²⁾ W_(i) ₁ _(+16,i) ₁_(+16,1) ⁽²⁾ W_(i) ₁ _(+24,i) ₁ _(+24,0) ⁽²⁾ W_(i) ₁ _(+24,i) ₁ _(+24,1)⁽²⁾ i₂ i₁ 8 9 10 11 0-15 {tilde over (W)}_(i) ₁ _(+8,i) ₁ _(+24,0) ⁽²⁾W_(i) ₁ _(+8,i) ₁ _(+24,0) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+24,2) ⁽²⁾ {tildeover (W)}_(i) ₁ _(+8,i) ₁ _(+24,2) ⁽²⁾ i₂ i₁ 12 13 14 15 0-15

where

${W_{m,m^{\prime},k}^{(2)} = {\frac{1}{\sqrt{8}}\begin{bmatrix}v_{m} & v_{m^{\prime}} \\{\varphi_{k}v_{m}} & {{- \varphi_{k}}v_{m^{\prime}}}\end{bmatrix}}},{{\overset{\sim}{W}}_{m,m^{\prime},k}^{(2)} = {\frac{1}{\sqrt{8}}\begin{bmatrix}v_{m} & v_{m^{\prime}} \\{\varphi_{k}v_{m}} & {\varphi_{k}v_{m^{\prime}}}\end{bmatrix}}},{{\overset{\overset{\sim}{\sim}}{W}}_{m,m^{\prime},k}^{(2)} = {\frac{1}{\sqrt{8}}\begin{bmatrix}v_{m} & v_{m^{\prime}} \\{\varphi_{k}v_{m^{\prime}}} & {{- \varphi_{k}}v_{m^{\prime}}}\end{bmatrix}}},{v_{m} = \begin{bmatrix}1 & e^{j\; 2\pi\;{m/32}}\end{bmatrix}},{v_{m^{\prime}} = \begin{bmatrix}1 & e^{j\; 2\pi\;{m^{\prime}/32}}\end{bmatrix}},$φ_(k)=e^(jπk/2), and m, m′, and k are nonnegative integers; i₁represents the first codebook index; i₂ represents the second codebookindex.

In this embodiment, optionally, when the rank determined by thedetermining module 110 is 1, the first PMI, the second PMI, the firstcodebook index corresponding to the first PMI, and the second codebookindex corresponding to the second PMI are determined according to TableC1, C2, C3, or C4:

TABLE C1 I_(PMI1) i₁ = I_(PMI1) I_(PMI2) i₂ 0 0 0 0 0 0 1 2 1 1 0 4 1 11 6 2 2 0 8 2 2 1 10 3 3 0 12 3 3 1 14 4 4 0 1 4 4 1 3 5 5 0 5 5 5 1 7 66 0 9 6 6 1 11 7 7 0 13 7 7 1 15

TABLE C2 I_(PMI1) i₁ = I_(PMI1) + 8 I_(PMI2) i₂ 0 8 0 0 0 8 1 2 1 9 0 41 9 1 6 2 10 0 8 2 10 1 10 3 11 0 12 3 11 1 14 4 12 0 1 4 12 1 3 5 13 05 5 13 1 7 6 14 0 9 6 14 1 11 7 15 0 13 7 15 1 15

TABLE C3 I_(PMI1) i₁ = 2I_(PMI1) I_(PMI2) i₂ 0 0 0 0 0 0 1 2 1 2 0 8 1 21 10 2 4 0 1 2 4 1 3 3 6 0 9 3 6 1 11 4 8 0 0 4 8 1 2 5 10 0 8 5 10 1 106 12 0 1 6 12 1 3 7 14 0 9 7 14 1 11

TABLE C4 I_(PMI1) i₁ = 2I_(PMI1) + 1 I_(PMI2) i₂ 0 1 0 4 0 1 1 6 1 3 012 1 3 1 14 2 5 0 5 2 5 1 7 3 7 0 13 3 7 1 15 4 9 0 4 4 9 1 6 5 11 0 125 11 1 14 6 13 0 5 6 13 1 7 7 15 0 13 7 15 1 15

where I_(PMI1) represents the first PMI, I_(PMI2) represents the secondPMI, i₁ represents the first codebook index, and i₂ represents thesecond codebook index.

In this embodiment, optionally, when the rank determined by thedetermining module 110 is 2, the value range of n may be the set {0, 1,2, 3, 4, 5, 6, 7} or {8, 9, 10, 11, 12, 13, 14, 15}.

In this embodiment, optionally, a value range of the first codebookindex corresponding to the first PMI and a value range of the secondcodebook index corresponding to the second PMI have an associationrelationship. Optionally, that a value range of the first codebook indexcorresponding to the first PMI and a value range of the second codebookindex corresponding to the second PMI have an association relationshipincludes: the value range of the second codebook index corresponding tothe second PMI is uniquely determined according to a value and/or thevalue range of the first codebook index corresponding to the first PMI.

It should be understood that the user equipment 100 according to thisembodiment may correspond to a user equipment that performs a method fortransmitting a 4-antenna precoding matrix according to an embodiment ofthe present invention, and the foregoing and other operations and/orfunctions of modules in the user equipment 100 are used to implement acorresponding procedure of the method in FIG. 1, which is not describedherein any further for brevity.

Therefore, by means of the user equipment according to this embodiment,more precoding matrices that are applicable to a uniform linear arrayantenna may be indicated without changing a feedback mode or feedbackbits, and it may also be ensured that performance for application of adual-polarized antenna is not affected, so that system performance maybe improved and user experience may be enhanced.

FIG. 8 shows a schematic block diagram of a user equipment 200 accordingto an embodiment. As shown in FIG. 8, the user equipment 200 includes: adetermining module 210, configured to determine a rank used forindicating the number of transmission layers, further configured todetermine a value of a first codebook index corresponding to oneprecoding matrix set in a codebook set, where the codebook setcorresponds to the rank, and precoding matrices included in the codebookset are represented by the first codebook index and a second codebookindex, and further configured to determine a jointly coded valuecorresponding to the rank and the value of the first codebook index,where the jointly coded value and the rank have a first correspondence,and the jointly coded value and the first codebook index have a secondcorrespondence; and a sending module 220, configured to send the jointlycoded value determined by the determining module 210 to a base station,where:

the precoding matrices W included in the codebook set satisfy thefollowing equation:

W=W₁×W₂, where

${W_{1} = \begin{bmatrix}X_{n} & 0 \\0 & X_{n}\end{bmatrix}},{X_{n} = \begin{bmatrix}1 & 1 & 1 & 1 \\q_{1}^{n} & q_{1}^{n + 8} & q_{1}^{n + 16} & q_{1}^{n + 24}\end{bmatrix}},$q₁=e^(j2π/32), and n=0, 1, . . . , 15; andthe first codebook index corresponds to one value of n, and a valuerange of n is a set {0, 1, 2, 3, 4, 5, 6, 7}, {8, 9, 10, 11, 12, 13, 14,15}, {0, 2, 4, 6}, {1, 3, 5, 7}, {8, 10, 12, 14}, or {9, 11, 13, 15}.

Therefore, the user equipment according to this embodiment may prevent aproblem where precoding matrices are repeated after subsampling, therebyimproving system performance and enhancing user experience.

In this embodiment, optionally, when the rank determined by thedetermining module 210 is 1, W₂ satisfies the following equation:

${W_{2} \in \left\{ {{\frac{1}{A}\begin{bmatrix}Y \\{{\alpha(i)}Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{j\;{\alpha(i)}Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{{- {\alpha(i)}}Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{{- j}\;{\alpha(i)}Y}\end{bmatrix}}} \right\}},$

where Yε{e₁,e₂,e₃,e₄}, α(i)=q₁ ^(2(i-1)); when Y is e₁, α(i) is α(1);when Y is e₂, α(i) is α(2); when Y is e₃, α(i) is α(3); when Y is e₄,α(i) is α(4); e_(i) represents a column vector with a dimension of 4×1,where an i^(th) element in e_(i) is 1, all other elements are 0, andiε{1, 2, 3, 4}; A is a constant.

In this embodiment, optionally, when the rank determined by thedetermining module 210 is 2, W₂ satisfies the following equation:

$\mspace{20mu}{W_{2} \in \left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}} \right\}}$(Y₁, Y₂) ∈ {(e₁, e₁), (e₂, e₂), (e₃, e₃), (e₄, e₄), (e₁, e₂), (e₂, e₃), (e₁, e₄), (e₂, e₄)};  or$W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & Y_{2}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{- Y_{1}} & Y_{2}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{- Y_{1}} & {- Y_{2}}\end{bmatrix}}} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ \left( {e_{2},e_{4}} \right) \right\}$$W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ {\left( {e_{1},e_{1}} \right),\left( {e_{2},e_{2}} \right),\left( {e_{3},e_{3}} \right),\left( {e_{4},e_{4}} \right)} \right\}$$W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{2} & {- Y_{1}}\end{bmatrix}},} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ {\left( {e_{1},e_{3}} \right),\left( {e_{2},e_{4}} \right),\left( {e_{3},e_{1}} \right),\left( {e_{4},e_{2}} \right)} \right\}$

where e_(i) represents a column vector with a dimension of 4×1, ani^(th) element in e_(i) is 1, all other elements are 0, and iε{1, 2, 3,4}; B is a constant.

In this embodiment, optionally, when the number of bits bearing thejointly coded value is 4, the correspondence between the jointly codedvalue and the rank and the correspondence between the jointly codedvalue and the first codebook index are determined according to thefollowing Table D:

TABLE D I_(RI/PMI1) RI i₁ 0-7 1 I_(RI/PMI1) 8-15 2 I_(RI/PMI1) − 8

where I_(RI/PMI1) represents the jointly coded value, RI represents therank, and i₁ represents the first codebook index.

In this embodiment, optionally, when the number of bits bearing thejointly coded value is 3, the correspondence between the jointly codedvalue and the rank and the correspondence between the jointly codedvalue and the first codebook index are determined according to thefollowing Table E:

TABLE E I_(RI/PMI1) RI i₁ 0-3 1 2 × I_(RI/PMI1) 4-7 2 2 × (I_(RI/PMI1) −4)

where I_(RI/PMI1) represents the jointly coded value, RI represents therank, and i₁ represents the first codebook index.

It should be understood that in this embodiment, when the rank isdetermined to be 1, the precoding matrices W included in the codebookset are determined according to Table A; it should be further understoodthat in this embodiment, when the rank determined by the UE is 2, theprecoding matrices W included in the codebook set are determinedaccording to Table B1 or B2. It should be understood that in thisembodiment, the jointly coded value represents a value generated byperforming joint coding on the rank and a first PMI, which is notdescribed herein any further for brevity.

In this embodiment, optionally, a value range of the first codebookindex corresponding to the first PMI and a value range of the secondcodebook index corresponding to a second PMI have an associationrelationship. Optionally, that a value range of the first codebook indexcorresponding to the first PMI and a value range of the second codebookindex corresponding to a second PMI have an association relationshipincludes the value range of the second codebook index corresponding tothe second PMI is uniquely determined according to a value and/or thevalue range of the first codebook index corresponding to the first PMI.

It should be understood that the user equipment 200 according to thisembodiment may correspond to a user equipment that performs a method fortransmitting a 4-antenna precoding matrix according to an embodiment,and the foregoing and other operations and/or functions of modules inthe user equipment 200 are used to implement a corresponding procedureof the method in FIG. 2, which is not described herein any further forbrevity.

Therefore, the user equipment according to this embodiment may prevent aproblem where precoding matrices are repeated after subsampling, therebyimproving system performance and enhancing user experience.

FIG. 9 shows a schematic block diagram of a user equipment 300 accordingto an embodiment. As shown in FIG. 9, the user equipment 300 includes: adetermining module 310, configured to determine a rank used forindicating the number of transmission layers, further configured todetermine a first precoding matrix in a codebook set corresponding tothe rank, where precoding matrices included in the codebook set arerepresented by a first codebook index and a second codebook index, andfurther configured to determine a second precoding matrix indicator PMIused for indicating the first precoding matrix, where the second PMI andthe second codebook index have a first correspondence, and for one givenfirst codebook index, a value range of the second codebook indexcorresponding to a value range of the second PMI is a proper subset of avalue range of the second codebook index; and a sending module 320,configured to send, to a base station, the second PMI that is used forindicating the first precoding matrix and determined by the determiningmodule 310, where:

the precoding matrices W included in the codebook set satisfy thefollowing equation:

W=W₁×W₂, where

${W_{1} = \begin{bmatrix}X_{n} & 0 \\0 & X_{n}\end{bmatrix}},{X_{n} = \begin{bmatrix}1 & 1 & 1 & 1 \\q_{1}^{n} & q_{1}^{n + 8} & q_{1}^{n + 16} & q_{1}^{n + 24}\end{bmatrix}},$q₁=e^(j2π/32), and n=0, 1, . . . , 15;

the first codebook index corresponds to one value of n, and a valuerange of n is a set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14,15}; and

when the rank determined by the determining module 310 is 2, inprecoding matrix sets that are determined according to the firstcodebook index and the second codebook index corresponding to the valuerange of the second PMI, a first precoding matrix set corresponding to afirst codebook index i_(1,a) and a second precoding matrix setcorresponding to a first codebook index i_(1,a+8) are mutuallyexclusive, where the first codebook index i_(1,a) represents a firstcodebook index corresponding to n whose value is a, the first codebookindex i_(1,a+8) represents a first codebook index corresponding to nwhose value is a+8, and aε{0, 1, 2, 3, 4, 5, 6, 7}.

Therefore, the user equipment according to this embodiment may prevent aproblem where precoding matrices are repeated after subsampling, therebyimproving system performance and enhancing user experience.

In this embodiment, optionally, when the rank determined by thedetermining module 310 is 1, W₂ satisfies the following equation:

${W_{2} \in \left\{ {{\frac{1}{A}\begin{bmatrix}Y \\{{\alpha(i)}Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{j\;{\alpha(i)}Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{{- {\alpha(i)}}Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{{- j}\;{\alpha(i)}Y}\end{bmatrix}}} \right\}},$

where Yε{e₁,e₂,e₃,e₄}, α(i)=q₁ ^(2(i-1)); when Y is e₁, α(i) is α(1);when Y is e₂, α(i) is α(2); when Y is e₃, α(i) is α(3); when Y is e₄,α(i) is α(4); e_(i) represents a column vector with a dimension of 4×1,where an i^(th) element in e_(i) is 1, all other elements are 0, andiε{1, 2, 3, 4}; A is a constant.

In this embodiment, optionally, when the rank determined by thedetermining module 310 is 2, W₂ satisfies the following equation:

$\mspace{20mu}{W_{2} \in \left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}} \right\}}$(Y₁, Y₂) ∈ {(e₁, e₁), (e₂, e₂), (e₃, e₃), (e₄, e₄), (e₁, e₂), (e₂, e₃), (e₁, e₄), (e₂, e₄)};  or$W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & Y_{2}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{- Y_{1}} & Y_{2}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{- Y_{1}} & {- Y_{2}}\end{bmatrix}}} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ \left( {e_{2},e_{4}} \right) \right\}$$W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ {\left( {e_{1},e_{1}} \right),\left( {e_{2},e_{2}} \right),\left( {e_{3},e_{3}} \right),\left( {e_{4},e_{4}} \right)} \right\}$$W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{2} & {- Y_{1}}\end{bmatrix}},} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ {\left( {e_{1},e_{3}} \right),\left( {e_{2},e_{4}} \right),\left( {e_{3},e_{1}} \right),\left( {e_{4},e_{2}} \right)} \right\}$

where e_(i) represents a column vector with a dimension of 4×1, ani^(th) element in e_(i) is 1, all other elements are 0, and iε{1, 2, 3,4}; B is a constant.

In this embodiment, optionally, when the rank determined by thedetermining module 310 is 2, mutual relationships between the secondPMI, the first codebook index, and the second codebook index aredetermined according to Table F1 or F2:

TABLE F1 I_(PMI2) i₁ i₂ 0-3 0-7 2 × I_(PMI2) 8-15 2 × I_(PMI2) + 1

TABLE F2 I_(PMI2) i₁ i₂ 0-3 0-7 2 × I_(PMI2) 8-15 2 × I_(PMI2) + 8

where I_(PMI2) represents the second PMI, i₁ represents the firstcodebook index, and i₂ represents the second codebook index.

In this embodiment, optionally, when the rank determined by thedetermining module 310 is 3 or 4, the precoding matrices included in thecodebook set corresponding to the rank are:

four precoding matrices with codebook indexes 0 to 3 in Table G; or

four precoding matrices with codebook indexes 4 to 7 in Table G; or

four precoding matrices with codebook indexes 12 to 15 in Table G,

TABLE G Codebook RI Index u_(n) 1 2 3 4 0 u₀ = [1 −1 −1 −1]^(T) W₀^({1}) W₀ ^({14})/{square root over (2)} W₀ ^({124})/{square root over(3)} W₀ ^({1234})/2 1 u₁ = [1 −j 1 j]^(T) W₁ ^({1}) W₁ ^({12})/{squareroot over (2)} W₁ ^({123})/{square root over (3)} W₁ ^({1234})/2 2 u₂ =[1 1 −1 1]^(T) W₂ ^({1}) W₂ ^({12})/{square root over (2)} W₂^({123})/{square root over (3)} W₂ ^({3214})/2 3 u₃ = [1 j 1 −j]^(T) W₃^({1}) W₃ ^({12})/{square root over (2)} W₃ ^({123})/{square root over(3)} W₃ ^({3214})/2 4 u₄ = [1 (−1 − j)/{square root over (2)} − j (1 −j)/{square root over (2)}]^(T) W₄ ^({1}) W₄ ^({14})/{square root over(2)} W₄ ^({124})/{square root over (3)} W₄ ^({1234})/2 5 u₅ = [1 (1 −j)/{square root over (2)} j (−1 − j)/{square root over (2)}]^(T) W₅^({1}) W₅ ^({14})/{square root over (2)} W₅ ^({124})/{square root over(3)} W₅ ^({1234})/2 6 u₆ = [1 (1 + j)/{square root over (2)} −j (−1 +j)/{square root over (2)}]^(T) W₆ ^({1}) W₆ ^({13})/{square root over(2)} W₆ ^({134})/{square root over (3)} W₆ ^({1324})/2 7 u₇ = [1 (−1 +j)/{square root over (2)} j (1 + j)/{square root over (2)}]^(T) W₇^({1}) W₇ ^({13})/{square root over (2)} W₇ ^({134})/{square root over(3)} W₇ ^({1324})/2 8 u₈ = [1 −1 1 1]^(T) W₈ ^({1}) W₈ ^({12})/{squareroot over (2)} W₈ ^({124})/{square root over (3)} W₈ ^({1234})/2 9 u₉ =[1 −j −1 −j]^(T) W₉ ^({1}) W₉ ^({14})/{square root over (2)} W₉^({134})/{square root over (3)} W₉ ^({1234})/2 10 u₁₀ = [1 1 1 −1]^(T)W₁₀ ^({1}) W₁₀ ^({13})/{square root over (2)} W₁₀ ^({123})/{square rootover (3)} W₁₀ ^({1324})/2 11 u₁₁ = [1 j −1 j]^(T) W₁₁ ^({1}) W₁₁^({13})/{square root over (2)} W₁₁ ^({134})/{square root over (3)} W₁₁^({1324})/2 12 u₁₂ = [1 −1 −1 1]^(T) W₁₂ ^({1}) W₁₂ ^({12})/{square rootover (2)} W₁₂ ^({123})/{square root over (3)} W₁₂ ^({1234})/2 13 u₁₃ =[1 −1 1 −1]^(T) W₁₃ ^({1}) W₁₃ ^({13})/{square root over (2)} W₁₃^({123})/{square root over (3)} W₁₃ ^({1324})/2 14 u₁₄ = [1 1 −1 −1]^(T)W₁₄ ^({1}) W₁₄ ^({13})/{square root over (2)} W₁₄ ^({123})/{square rootover (3)} W₁₄ ^({3214})/2 15 u₁₅ = [1 1 1 1]^(T) W₁₅ ^({1}) W₁₅^({12})/{square root over (2)} W₁₅ ^({123})/{square root over (3)} W₁₅^({1234})/2

where W_(n) ^({s}) represents a matrix formed by a column set {s} of amatrix W_(n)=I−2u_(n)u_(n) ^(H)/u_(n) ^(H)u_(n), and I is a 4×4 identitymatrix.

It should be understood that in this embodiment, when the rank isdetermined to be 1, the precoding matrices W included in the codebookset are determined according to Table A; it should be further understoodthat in this embodiment, when the rank determined by the UE is 2, theprecoding matrices W included in the codebook set are determinedaccording to Table B1 or B2. It should be understood that in thisembodiment, the jointly coded value represents a value generated byperforming joint coding on the rank and a first PMI, which is notdescribed herein any further for brevity.

In this embodiment, optionally, a value range of the first codebookindex corresponding to the first PMI and the value range of the secondcodebook index corresponding to the second PMI have an associationrelationship. Optionally, that a value range of the first codebook indexcorresponding to the first PMI and the value range of the secondcodebook index corresponding to the second PMI have an associationrelationship includes: the value range of the second codebook indexcorresponding to the second PMI is uniquely determined according to avalue and/or the value range of the first codebook index correspondingto the first PMI.

It should be understood that the user equipment 300 according to thisembodiment may correspond to a user equipment that performs a method fortransmitting a 4-antenna precoding matrix according to an embodiment,and the foregoing and other operations and/or functions of modules inthe user equipment 300 are used to implement a corresponding procedureof the method in FIG. 3, which is not described herein any further forbrevity.

Therefore, the user equipment according to this embodiment may prevent aproblem where precoding matrices are repeated after subsampling, therebyimproving system performance and enhancing user experience.

FIG. 10 shows a schematic block diagram of a base station 600 accordingto an embodiment. As shown in FIG. 10, the base station 600 includes areceiving module 610, configured to receive a rank used for indicatingthe number of transmission layers, a first precoding matrix indicatorPMI, and a second PMI that are sent by a user equipment. Also includedis a determining module 620, configured to determine, according to thefirst PMI and the second PMI received by the receiving module 610, afirst precoding matrix in a codebook set corresponding to the rankreceived by the receiving module 610, where precoding matrices includedin the codebook set are represented by a first codebook index and asecond codebook index, the first PMI and the first codebook index have afirst correspondence, and the second PMI and the second codebook indexhave a second correspondence, where the precoding matrices W included inthe codebook set satisfy the following equation:

W=W₁×W₂, where

${W_{1} = \begin{bmatrix}X_{n} & 0 \\0 & X_{n}\end{bmatrix}},{X_{n} = \begin{bmatrix}1 & 1 & 1 & 1 \\q_{1}^{n} & q_{1}^{n + 8} & q_{1}^{n + 16} & q_{1}^{n + 24}\end{bmatrix}},{q_{1} = e^{j\; 2{\pi/32}}},$and n=0, 1, . . . , 15; and

the first codebook index corresponds to one value of n, and a valuerange of n is a set {0, 1, 2, 3, 4, 5, 6, 7}, {8, 9, 10, 11, 12, 13, 14,15}, {0, 2, 4, 6, 8, 10, 12, 14}, or {1, 3, 5, 7, 9, 11, 13, 15}.

Therefore, by means of the base station according to this embodiment,more precoding matrices that are applicable to a uniform linear arrayantenna may be indicated without changing a feedback mode or feedbackbits, and it may also be ensured that performance for application of adual-polarized antenna is not affected, so that system performance maybe improved and user experience may be enhanced.

In this embodiment, optionally, a value range of the first codebookindex i₁ is 0≦i₁≦15, and a value range of the second codebook index i₂is 0≦i₂≦L₂−1, where L₂ is a positive integer. For example, a value rangeof L₂ is 1≦L₂≦16, that is, the value range of the second codebook indexi₂ is, for example, 0≦i₂≦15.

In this embodiment, optionally, when the rank received by the receivingmodule 610 is 1, W₂ satisfies the following equation:

${W_{2} \in \left\{ {{\frac{1}{A}\begin{bmatrix}Y \\{{\alpha(i)}Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{j\;{\alpha(i)}Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{{- {\alpha(i)}}Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{{- j}\;{\alpha(i)}Y}\end{bmatrix}}} \right\}},$

where Yε{e₁,e₂,e₃,e₄}, α(i)=q₁ ^(2(i-1)); when Y is e₁, α(i) is α(1);when Y is e₂, α(i) is α(2); when Y is e₃, α(i) is α(3); when Y is e₄,α(i) is α(4); e_(i) represents a column vector with a dimension of 4×1,where an i^(th) element in e_(i) is 1, all other elements are 0, andiε{1, 2, 3, 4}; A is a constant.

In this embodiment, optionally, when the rank received by the receivingmodule 610 is 2, W₂ satisfies the following equation:

$\mspace{20mu}{W_{2} \in \left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}} \right\}}$(Y₁, Y₂) ∈ {(e₁, e₁), (e₂, e₂), (e₃, e₃), (e₄, e₄), (e₁, e₂), (e₂, e₃), (e₁, e₄), (e₂, e₄)};  or$W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & Y_{2}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{- Y_{1}} & Y_{2}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{- Y_{1}} & {- Y_{2}}\end{bmatrix}}} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ \left( {e_{2},e_{4}} \right) \right\}$$W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ {\left( {e_{1},e_{1}} \right),\left( {e_{2},e_{2}} \right),\left( {e_{3},e_{3}} \right),\left( {e_{4},e_{4}} \right)} \right\}$$W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{2} & {- Y_{1}}\end{bmatrix}},} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ {\left( {e_{1},e_{3}} \right),\left( {e_{2},e_{4}} \right),\left( {e_{3},e_{1}} \right),\left( {e_{4},e_{2}} \right)} \right\}$

where e_(i) represents a column vector with a dimension of 4×1, ani^(th) element in e_(i) is 1, all other elements are 0, and iε{1, 2, 3,4}; B is a constant.

In this embodiment, optionally, a precoding matrix set corresponding tothe first codebook index corresponding to the first PMI includesprecoding matrices U1 and U2, where the precoding matrices U1 and U2 areindicated by the second codebook index, where:

${{U\; 1} = {\frac{1}{A}\begin{bmatrix}v \\{\beta\; v}\end{bmatrix}}},{{U\; 2} = {\frac{1}{A}\begin{bmatrix}v \\{{- \beta}\; v}\end{bmatrix}}},{v = \begin{bmatrix}1 \\q_{1}^{n + {({8n\mspace{14mu}{mod}\mspace{14mu} 32})}}\end{bmatrix}},$β=j^(└n/4┘)*α(i), i=(n mod 4)+1, α(i)=q₁ ^(2(i-1)), and A is a constant.

In this embodiment, optionally, when the rank received by the receivingmodule 610 is 1, the precoding matrices W included in the codebook setare determined according to Table A:

TABLE A i₂ i₁ 0 1 2 3 0-15 W_(i) ₁ _(,0) ⁽¹⁾ W_(i) ₁ _(,1) ⁽¹⁾ W_(i) ₁_(,2) ⁽¹⁾ W_(i) ₁ _(,3) ⁽¹⁾ i₂ i₁ 4 5 6 7 0-15 W_(i) ₁ _(+8,0) ⁽¹⁾ W_(i)₁ _(+8,1) ⁽¹⁾ W_(i) ₁ _(+8,2) ⁽¹⁾ W_(i) ₁ _(+8,3) ⁽¹⁾ i₂ i₁ 8 9 10 110-15 W_(i) ₁ _(+16,0) ⁽¹⁾ W_(i) ₁ _(+16,1) ⁽¹⁾ W_(i) ₁ _(+16,2) ⁽¹⁾W_(i) ₁ _(+16,3) ⁽¹⁾ i₂ i₁ 12 13 14 15 0-15 W_(i) ₁ _(+24,0) ⁽¹⁾ W_(i) ₁_(+24,1) ⁽¹⁾ W_(i) ₁ _(+24,2) ⁽¹⁾ W_(i) ₁ _(+24,3) ⁽¹⁾

where

${W_{m,k}^{(1)} = {\frac{1}{2}\begin{bmatrix}v \\{\varphi_{k}{\gamma(m)}v_{m}}\end{bmatrix}}},{{\gamma(m)} = e^{j\; 2\pi\frac{{({m - i_{1}})}/4}{32}}},{v_{m} = \begin{bmatrix}1 & e^{j\; 2\;\pi\;{m/32}}\end{bmatrix}},$φ_(k)=e^(jπk/2), and m and k are nonnegative integers; i₁ represents thefirst codebook index; i₂ represents the second codebook index.

In this embodiment, optionally, when the rank received by the receivingmodule 610 is 2, the precoding matrices W included in the codebook setare determined according to Table B1 or B2:

TABLE B1 i₂ i₁ 0 1 2 3 0-15 W_(i) ₁ _(,i) ₁ _(,0) ⁽²⁾ W_(i) ₁ _(,i) ₁_(,1) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+8,0) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+8,1) ⁽²⁾ i₂i₁ 4 5 6 7 0-15 W_(i) ₁ _(+16,i) ₁ _(+16,0) ⁽²⁾ W_(i) ₁ _(+16,i) ₁_(+16,1) ⁽²⁾ W_(i) ₁ _(+24,i) ₁ _(+24,0) ⁽²⁾ W_(i) ₁ _(+24,i) ₁ _(+24,1)⁽²⁾ i₂ i₁ 8 9 10 11 0-15 W_(i) ₁ _(,i) ₁ _(+8,0) ⁽²⁾ W_(i) ₁ _(,i) ₁_(+8,1) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+16,0) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+16,1)⁽²⁾ i₂ i₁ 12 13 14 15 0-15 W_(i) ₁ _(,i) ₁ _(+24,0) ⁽²⁾ W_(i) ₁ _(,i) ₁_(+24,1) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+24,0) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+24,1)⁽²⁾

i₂ i₁ 0 1 2 3 0-15 W_(i) ₁ _(,i) ₁ _(,0) ⁽²⁾ W_(i) ₁ _(,i) ₁ _(,1) ⁽²⁾W_(i) ₁ _(+8,i) ₁ _(+8,0) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+8,1) ⁽²⁾ i₂ i₁ 4 5 67 0-15 W_(i) ₁ _(+16,i) ₁ _(+16,0) ⁽²⁾ W_(i) ₁ _(+16,i) ₁ _(+16,1) ⁽²⁾W_(i) ₁ _(+24,i) ₁ _(+24,0) ⁽²⁾ W_(i) ₁ _(+24,i) ₁ _(+24,1) ⁽²⁾ i₂ i₁ 89 10 11 0-15 {tilde over (W)}_(i) ₁ _(+8,i) ₁ _(+24,0) ⁽²⁾ W_(i) ₁_(,+8,i) ₁ _(+24,0) ⁽²⁾ W_(i) ₁ _(+8,i) ₁ _(+24,2) ⁽²⁾ {tilde over(W)}_(i) ₁ _(+8,i) ₁ _(+24,2) ⁽²⁾ i₂ i₁ 12 13 14 15 0-15

where

${W_{m,m^{\prime},k}^{(2)} = {\frac{1}{\sqrt{8}}\begin{bmatrix}v_{m} & v_{m^{\prime}} \\{\varphi_{k}v_{m}} & {{- \varphi_{k}}v_{m^{\prime}}}\end{bmatrix}}},{{\overset{\sim}{W}}_{m,m^{\prime},k}^{(2)} = {\frac{1}{\sqrt{8}}\begin{bmatrix}v_{m} & v_{m^{\prime}} \\{\varphi_{k}v_{m}} & {\varphi_{k}v_{m^{\prime}}}\end{bmatrix}}},{{\overset{\overset{\sim}{\sim}}{W}}_{m,m^{\prime},k}^{(2)} = {\frac{1}{\sqrt{8}}\begin{bmatrix}v_{m} & v_{m^{\prime}} \\{\varphi_{k}v_{m^{\prime}}} & {{- \varphi_{k}}v_{m}}\end{bmatrix}}},{v_{m} = \begin{bmatrix}1 & e^{j\; 2\pi\;{m/32}}\end{bmatrix}},{v_{m^{\prime}} = \begin{bmatrix}1 & e^{j\; 2\pi\;{m^{\prime}/32}}\end{bmatrix}},$φ_(k)=e^(jπk/2), and m, m′, and k are nonnegative integers; i₁represents the first codebook index; i₂ represents the second codebookindex.

In this embodiment, optionally, when the rank received by the receivingmodule 610 is 1, the first PMI, the second PMI, the first codebook indexcorresponding to the first PMI, and the second codebook indexcorresponding to the second PMI are determined according to Table C1,C2, C3, or C4:

TABLE C1 I_(PMI1) i₁ = I_(PMI1) I_(PMI2) i₂ 0 0 0 0 0 0 1 2 1 1 0 4 1 11 6 2 2 0 8 2 2 1 10 3 3 0 12 3 3 1 14 4 4 0 1 4 4 1 3 5 5 0 5 5 5 1 7 66 0 9 6 6 1 11 7 7 0 13 7 7 1 15

TABLE C2 I_(PMI1) i₁ = I_(PMI1) + 8 I_(PMI2) i₂ 0 8 0 0 0 8 1 2 1 9 0 41 9 1 6 2 10 0 8 2 10 1 10 3 11 0 12 3 11 1 14 4 12 0 1 4 12 1 3 5 13 05 5 13 1 7 6 14 0 9 6 14 1 11 7 15 0 13 7 15 1 15

TABLE C3 I_(PMI1) i₁ = 2I_(PMI1) I_(PMI2) i₂ 0 0 0 0 0 0 1 2 1 2 0 8 1 21 10 2 4 0 1 2 4 1 3 3 6 0 9 3 6 1 11 4 8 0 0 4 8 1 2 5 10 0 8 5 10 1 106 12 0 1 6 12 1 3 7 14 0 9 7 14 1 11

TABLE C4 I_(PMI1) i₁ = 2I_(PMI1) + 1 I_(PMI2) i₂ 0 1 0 4 0 1 1 6 1 3 012 1 3 1 14 2 5 0 5 2 5 1 7 3 7 0 13 3 7 1 15 4 9 0 4 4 9 1 6 5 11 0 125 11 1 14 6 13 0 5 6 13 1 7 7 15 0 13 7 15 1 15

where I_(PMI1) represents the first PMI, I_(PMI2) represents the secondPMI, i₁ represents the first codebook index, and i₂ represents thesecond codebook index.

In this embodiment, optionally, when the rank received by the receivingmodule 610 is 2, the value range of n may be the set {0, 1, 2, 3, 4, 5,6, 7} or {8, 9, 10, 11, 12, 13, 14, 15}.

In this embodiment, optionally, a value range of the first codebookindex corresponding to the first PMI and a value range of the secondcodebook index corresponding to the second PMI have an associationrelationship. Optionally, that a value range of the first codebook indexcorresponding to the first PMI and a value range of the second codebookindex corresponding to the second PMI have an association relationshipincludes: the value range of the second codebook index corresponding tothe second PMI is uniquely determined according to a value and/or thevalue range of the first codebook index corresponding to the first PMI.

It should be understood that the base station 600 according to thisembodiment may correspond to a base station that performs a method fortransmitting a precoding matrix according to an embodiment, and theforegoing and other operations and/or functions of modules in the basestation 600 are used to implement a corresponding procedure of themethod in FIG. 4, which is not described herein any further for brevity.

Therefore, by means of the base station according to this embodiment,more precoding matrices that are applicable to a uniform linear arrayantenna may be indicated without changing a feedback mode or feedbackbits, and it may also be ensured that performance for application of adual-polarized antenna is not affected, so that system performance maybe improved and user experience may be enhanced.

FIG. 11 shows a schematic block diagram of a base station 700 accordingto an embodiment of the present invention. As shown in FIG. 11, the basestation 700 includes a receiving module 710, configured to receive ajointly coded value sent by a user equipment. Also included is adetermining module 720, configured to determine a value of a firstcodebook index and a rank used for indicating the number of transmissionlayers according to the jointly coded value received by the receivingmodule 710, a correspondence between the jointly coded value and therank and a correspondence between the jointly coded value and the firstcodebook index, where: the value of the first codebook index correspondsto one precoding matrix set in a codebook set, the codebook setcorresponds to the rank, precoding matrices included in the codebook setare represented by the first codebook index and a second codebook index,and the precoding matrices W included in the codebook set satisfy thefollowing equation:

W=W₁×W₂, where

${W_{1} = \begin{bmatrix}X_{n} & 0 \\0 & X_{n}\end{bmatrix}},{X_{n} = \begin{bmatrix}1 & 1 & 1 & 1 \\q_{1}^{n} & q_{1}^{n + 8} & q_{1}^{n + 16} & q_{1}^{n + 24}\end{bmatrix}},$q₁=e^(j2π/32), and n=0, 1, . . . , 15; and

the first codebook index corresponds to one value of n, and a valuerange of n is a set {0, 1, 2, 3, 4, 5, 6, 7}, {8, 9, 10, 11, 12, 13, 14,15}, {0, 2, 4, 6}, {1, 3, 5, 7}, {8, 10, 12, 14}, or {9, 11, 13, 15}.

Therefore, the base station according to this embodiment may prevent aproblem where precoding matrices are repeated after subsampling, therebyimproving system performance and enhancing user experience.

In this embodiment, optionally, a value range of the first codebookindex i₁ is 0≦i₁≦15, and a value range of the second codebook index i₂is 0≦i₂≦L₂−1, where L₂ is a positive integer. For example, a value rangeof L₂ is 1≦L₂≦16, that is, the value range of the second codebook indexi₂ is, for example, 0≦i₂≦15.

In this embodiment, optionally, when the rank determined by thedetermining module 720 is 1, W₂ satisfies the following equation:

${W_{2} \in \left\{ {{\frac{1}{A}\begin{bmatrix}Y \\{{\alpha(i)}Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{j\;{\alpha(i)}Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{{- {\alpha(i)}}Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{{- j}\;{\alpha(i)}Y}\end{bmatrix}}} \right\}},$

where Yε{e₁,e₂,e₃,e₄}, α(i)=q₁ ^(2(i-1)); when Y is e₁, α(i) is α(1);when Y is e₂, α(i) is α(2); when Y is e₃, α(i) is α(3); when Y is e₄,α(i) is α(4); e_(i) represents a column vector with a dimension of 4×1,where an i^(th) element in e_(i) is 1, all other elements are 0, andiε{1, 2, 3, 4}; A is a constant.

In this embodiment, optionally, when the rank determined by thedetermining module 720 is 2, W₂ satisfies the following equation:

$\mspace{20mu}{W_{2} \in \left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}} \right\}}$(Y₁, Y₂) ∈ {(e₁, e₁), (e₂, e₂), (e₃, e₃), (e₄, e₄), (e₁, e₂), (e₂, e₃), (e₁, e₄), (e₂, e₄)} ;  or$W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & Y_{2}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{- Y_{1}} & Y_{2}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{- Y_{1}} & {- Y_{2}}\end{bmatrix}}} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ \left( {e_{2},e_{4}} \right) \right\}$$W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ {\left( {e_{1},e_{1}} \right),\left( {e_{2},e_{2}} \right),\left( {e_{3},e_{3}} \right),\left( {e_{4},e_{4}} \right)} \right\}$$W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{2} & {- Y_{1}}\end{bmatrix}},} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ {\left( {e_{1},e_{3}} \right),\left( {e_{2},e_{4}} \right),\left( {e_{3},e_{1}} \right),\left( {e_{4},e_{2}} \right)} \right\}$

where e_(i) represents a column vector with a dimension of 4×1, ani^(th) element in e_(i) is 1, all other elements are 0, and iε{1, 2, 3,4}; B is a constant.

In this embodiment, optionally, when the number of bits bearing thejointly coded value is 4, the correspondence between the jointly codedvalue and the rank and the correspondence between the jointly codedvalue and the first codebook index are determined according to thefollowing Table D:

TABLE D I_(RI/PMI1) RI i₁ 0-7 1 I_(RI/PMI1) 8-15 2 I_(RI/PMI1) − 8

where I_(RI/PMI1) represents the jointly coded value, RI represents therank, and i₁ represents the first codebook index.

In this embodiment, optionally, when the number of bits bearing thejointly coded value is 3, the correspondence between the jointly codedvalue and the rank and the correspondence between the jointly codedvalue and the first codebook index are determined according to thefollowing Table E:

TABLE E I_(RI/PMI1) RI i₁ 0-3 1 2 × I_(RI/PMI1) 4-7 2 2 × (I_(RI/PMI1) −4)

where I_(RI/PMI1) represents the jointly coded value, RI represents therank, and i₁ represents the first codebook index.

It should be understood that in this embodiment, when the rank isdetermined to be 1, the precoding matrices W included in the codebookset are determined according to Table A; it should be further understoodthat in this embodiment, when the rank determined by the UE is 2, theprecoding matrices W included in the codebook set are determinedaccording to Table B1 or B2. It should be understood that in thisembodiment, the jointly coded value represents a value generated byperforming joint coding on the rank and a first PMI, which is notdescribed herein any further for brevity.

In this embodiment, optionally, a value range of the first codebookindex corresponding to the first PMI and a value range of the secondcodebook index corresponding to a second PMI have an associationrelationship. Optionally, that a value range of the first codebook indexcorresponding to the first PMI and a value range of the second codebookindex corresponding to a second PMI have an association relationshipincludes: the value range of the second codebook index corresponding tothe second PMI is uniquely determined according to a value and/or thevalue range of the first codebook index corresponding to the first PMI.

It should be understood that the base station 700 according to thisembodiment may correspond to a base station that performs a method fortransmitting a precoding matrix according to an embodiment of thepresent invention, and the foregoing and other operations and/orfunctions of modules in the base station 700 are used to implement acorresponding procedure of the method in FIG. 5, which is not describedherein any further for brevity.

Therefore, the base station according to this embodiment may prevent aproblem where precoding matrices are repeated after subsampling, therebyimproving system performance and enhancing user experience.

FIG. 12 shows a schematic block diagram of a base station 800 accordingto an embodiment of the present invention. As shown in FIG. 12, the basestation 800 includes a receiving module 810, configured to receive asecond precoding matrix indicator PMI, a first codebook index, and arank used for indicating the number of transmission layers that are sentby a user equipment. Also included is a determining module 820,configured to determine, according to the second PMI and the firstcodebook index received by the receiving module 810, a first precodingmatrix in a codebook set corresponding to the rank received by thereceiving module 810, where precoding matrices included in the codebookset are represented by the first codebook index and a second codebookindex, the second PMI and the second codebook index have a firstcorrespondence, and for one given first codebook index, a value range ofthe second codebook index corresponding to a value range of the secondPMI is a proper subset of a value range of the second codebook index,where the precoding matrices W included in the codebook set satisfy thefollowing equation:

W=W₁×W₂, where

${W_{1} = \begin{bmatrix}X_{n} & 0 \\0 & X_{n}\end{bmatrix}},{X_{n} = \begin{bmatrix}1 & 1 & 1 & 1 \\q_{1}^{n} & q_{1}^{n + 8} & q_{1}^{n + 16} & q_{1}^{n + 24}\end{bmatrix}},$q₁=e^(j2π/32), and n=0, 1, . . . , 15;

the first codebook index corresponds to one value of n, and a valuerange of n is a set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14,15}; and

when the received rank is 2, in precoding matrix sets that aredetermined according to the first codebook index and the second codebookindex corresponding to the value range of the second PMI, a firstprecoding matrix set corresponding to a first codebook index i_(1,a) anda second precoding matrix set corresponding to a first codebook indexi_(1,a+8) are mutually exclusive, where the first codebook index i_(1,a)represents a first codebook index corresponding to n whose value is a,the first codebook index i_(1,a+8) represents a first codebook indexcorresponding to n whose value is a+8, and aε{0, 1, 2, 3, 4, 5, 6, 7}.

Therefore, the base station according to this embodiment may prevent aproblem where precoding matrices are repeated after subsampling, therebyimproving system performance and enhancing user experience.

In this embodiment, optionally, when the rank received by the receivingmodule 810 is 1, W₂ satisfies the following equation:

${W_{2} \in \left\{ {{\frac{1}{A}\begin{bmatrix}Y \\{{\alpha(i)}Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{j\;{\alpha(i)}Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{{- {\alpha(i)}}Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{{- j}\;{\alpha(i)}Y}\end{bmatrix}}} \right\}},$

where Yε{e₁,e₂,e₃,e₄}, α(i)=q₁ ^(2(i-1)); when Y is e₁, α(i) is α(1);when Y is e₂, α(i) is α(2); when Y is e₃, α(i) is α(3); when Y is e₄,α(i) is α(4); e_(i) represents a column vector with a dimension of 4×1,where an i^(th) element in e_(i) is 1, all other elements are 0, andiε{1, 2, 3, 4}; A is a constant.

In this embodiment, optionally, when the rank received by the receivingmodule 810 is 2, W₂ satisfies the following equation:

$\mspace{20mu}{W_{2} \in \left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}} \right\}}$(Y₁, Y₂) ∈ {(e₁, e₁), (e₂, e₂), (e₃, e₃), (e₄, e₄), (e₁, e₂), (e₂, e₃), (e₁, e₄), (e₂, e₄)}; or$W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & Y_{2}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{- Y_{1}} & Y_{2}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{- Y_{1}} & {- Y_{2}}\end{bmatrix}}} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ \left( {e_{2},e_{4}} \right) \right\}$$W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ {\left( {e_{1},e_{1}} \right),\left( {e_{2},e_{2}} \right),\left( {e_{3},e_{3}} \right),\left( {e_{4},e_{4}} \right)} \right\}$$W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{2} & {- Y_{1}}\end{bmatrix}},} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ {\left( {e_{1},e_{3}} \right),\left( {e_{2},e_{4}} \right),\left( {e_{3},e_{1}} \right),\left( {e_{4},e_{2}} \right)} \right\}$

where e_(i) represents a column vector with a dimension of 4×1, ani^(th) element in e_(i) is 1, all other elements are 0, and iε{1, 2, 3,4}; B is a constant.

In this embodiment, optionally, when the rank received by the receivingmodule 810 is 2, mutual relationships between the second PMI, the firstcodebook index, and the second codebook index are determined accordingto Table F1 or F2:

TABLE F1 I_(PMI2) i₁ i₂ 0-3 0-7  2 × I_(PMI2) 8-15 2 × I_(PMI2) + 1

TABLE F2 I_(PMI2) i₁ i₂ 0-3 0-7 2 × I_(PMI2) 8-15 2 × I_(PMI2) + 8

where I_(PMI2) represents the second PMI, i₁ represents the firstcodebook index, and i₂ represents the second codebook index.

In this embodiment, optionally, when the rank received by the receivingmodule 810 is 3 or 4, the precoding matrices included in the codebookset corresponding to the rank are:

four precoding matrices with codebook indexes 0 to 3 in Table G; or

four precoding matrices with codebook indexes 4 to 7 in Table G; or

four precoding matrices with codebook indexes 12 to 15 in Table G,

TABLE G Codebook RI Index u_(n) 1 2 3 4 0 u₀ = [1 −1 −1 −1]^(T) W₀^({1}) W₀ ^({14})/{square root over (2)} W₀ ^({124})/{square root over(3)} W₀ ^({1234})/2 1 u₁ = [1 −j 1 j]^(T) W₁ ^({1}) W₁ ^({12})/{squareroot over (2)} W₁ ^({123})/{square root over (3)} W₁ ^({1234})/2 2 u₂ =[1 1 −1 1]^(T) W₂ ^({1}) W₂ ^({12})/{square root over (2)} W₂^({123})/{square root over (3)} W₂ ^({ 3214})/2 3 u₃ = [1 j 1 −j]^(T) W₃^({1}) W₃ ^({12})/{square root over (2)} W₃ ^({123})/{square root over(3)} W₃ ^({ 3214})/2 4 u₄ = [1 (−1 − j)/{square root over (2)} −j (1 −j)/{square root over (2)}]^(T) W₄ ^({1}) W₄ ^({14})/{square root over(2)} W₄ ^({124})/{square root over (3)} W₄ ^({1234})/2 5 u₅ = [1 (1 −j)/{square root over (2)} j (−1 − j)/{square root over (2)}]^(T) W₅^({1}) W₅ ^({14})/{square root over (2)} W₅ ^({124})/{square root over(3)} W₅ ^({1234})/2 6 u₆ = [1 (1 + j)/{square root over (2)} −j (−1 +j)/{square root over (2)}]^(T) W₆ ^({1}) W₆ ^({13})/{square root over(2)} W₆ ^({134})/{square root over (3)} W₆ ^({1324})/2 7 u₇ = [1 (−1 +j)/{square root over (2)} j (1 + j)/{square root over (2)}]^(T) W₇^({1}) W₇ ^({13})/{square root over (2)} W₇ ^({134})/{square root over(3)} W₇ ^({1324})/2 8 u₈ = [1 −1 1 1]^(T) W₈ ^({1}) W₈ ^({12})/{squareroot over (2)} W₈ ^({124})/{square root over (3)} W₈ ^({1234})/2 9 u₉ =[1 −j −1 −j]^(T) W₉ ^({1}) W₉ ^({14})/{square root over (2)} W₉^({134})/{square root over (3)} W₉ ^({1234})/2 10 u₁₀ = [1 1 1 −1]^(T)W₁₀ ^({1}) W₁₀ ^({13})/{square root over (2)} W₁₀ ^({123})/{square rootover (3)} W₁₀ ^({1324})/2 11 u₁₁ = [1 j −1 j]^(T) W₁₁ ^({1}) W₁₁^({13})/{square root over (2)} W₁₁ ^({134})/{square root over (3)} W₁₁^({1324})/2 12 u₁₂ = [1 −1 −1 1]^(T) W₁₂ ^({1}) W₁₂ ^({12})/{square rootover (2)} W₁₂ ^({123})/{square root over (3)} W₁₂ ^({1234})/2 13 u₁₃ =[1 −1 1 −1]^(T) W₁₃ ^({1}) W₁₃ ^({13})/{square root over (2)} W₁₃^({123})/{square root over (3)} W₁₃ ^({1324})/2 14 u₁₄ = [1 1 −1 −1]^(T)W₁₄ ^({1}) W₁₄ ^({13})/{square root over (2)} W₁₄ ^({123})/{square rootover (3)} W₁₄ ^({ 3214})/2 15 u₁₅ = [1 1 1 1]^(T) W₁₅ ^({1}) W₁₅^({12})/{square root over (2)} W₁₅ ^({123})/{square root over (3)} W₁₅^({1234})/2

where W_(n) ^({s}) represents a matrix formed by a column set {s} of amatrix W_(n)=I−2u_(n)u_(n) ^(H)/u_(n) ^(H)u_(n), and I is a 4×4 identitymatrix.

It should be understood that in this embodiment, when the rank isdetermined to be 1, the precoding matrices W included in the codebookset are determined according to Table A; it should be further understoodthat in this embodiment, when the rank determined by the UE is 2, theprecoding matrices W included in the codebook set are determinedaccording to Table B1 or B2. It should be understood that in thisembodiment, the jointly coded value represents a value generated byperforming joint coding on the rank and a first PMI, which is notdescribed herein any further for brevity.

In this embodiment, optionally, a value range of the first codebookindex corresponding to the first PMI and the value range of the secondcodebook index corresponding to the second PMI have an associationrelationship. Optionally, that a value range of the first codebook indexcorresponding to the first PMI and the value range of the secondcodebook index corresponding to the second PMI have an associationrelationship includes: the value range of the second codebook indexcorresponding to the second PMI is uniquely determined according to avalue and/or the value range of the first codebook index correspondingto the first PMI.

It should be understood that the base station 800 according to thisembodiment may correspond to a base station that performs a method fortransmitting a precoding matrix according to an embodiment, and theforegoing and other operations and/or functions of modules in the basestation 800 are used to implement a corresponding procedure of themethod in FIG. 6, which is not described herein any further for brevity.

Therefore, the base station according to this embodiment may prevent aproblem where precoding matrices are repeated after subsampling, therebyimproving system performance and enhancing user experience.

In addition, the terms “system” and “network” may be usedinterchangeably in this specification. The term “and/or” in thisspecification describes only an association relationship for describingassociated objects and represents that three relationships may exist.For example, A and/or B may represent the following three cases: Only Aexists, both A and B exist, and only B exists.

It should be understood that in this embodiment, “B corresponding to A”represents that B and A are associated and B may be determined accordingto A. However, it should be further understood that determining Baccording to A does not mean that B is determined only according to Aand B may be further determined according to A and/or other information.

As shown in FIG. 13, an embodiment further provides a user equipment1000. The user equipment 1000 includes a processor 1100, a memory 1200,a bus system 1300, and a transmitter 1400. The processor 1100, thememory 1200, and the transmitter 1400 are connected by using the bussystem 1300; the memory 1200 is configured to store an instruction, andthe processor 1100 is configured to execute the instruction stored bythe memory 1200, so as to control the transmitter 1400 to transmit asignal. The processor 1100 is configured to determine a rank used forindicating the number of transmission layers; determine a firstprecoding matrix in a codebook set corresponding to the rank, whereprecoding matrices included in the codebook set are represented by afirst codebook index and a second codebook index; and determine a firstprecoding matrix indicator PMI and a second PMI used for indicating thefirst precoding matrix, where the first PMI and the first codebook indexhave a first correspondence, and the second PMI and the second codebookindex have a second correspondence. The transmitter 1400 is configuredto send the first PMI and the second PMI used for indicating the firstprecoding matrix to a base station, where the precoding matrices Wincluded in the codebook set satisfy the following equation:

W=W₁×W₂, where

${W_{1} = \begin{bmatrix}X_{n} & 0 \\0 & X_{n}\end{bmatrix}},{X_{n} = \begin{bmatrix}1 & 1 & 1 & 1 \\q_{1}^{n} & q_{1}^{n + 8} & q_{1}^{n + 16} & q_{1}^{n + 24}\end{bmatrix}},$q₁=e^(j2π/32), and n=0, 1, . . . , 15; and

the first codebook index corresponds to one value of n, and a valuerange of n is a set {0, 1, 2, 3, 4, 5, 6, 7}, {8, 9, 10, 11, 12, 13, 14,15}, {0, 2, 4, 6, 8, 10, 12, 14}, or {1, 3, 5, 7, 9, 11, 13, 15}.

Therefore, by means of the user equipment according to this embodimentof the present invention, more precoding matrices that are applicable toa uniform linear array antenna may be indicated without changing afeedback mode or feedback bits, and it may also be ensured thatperformance for application of a dual-polarized antenna is not affected,so that system performance may be improved and user experience may beenhanced.

It should be understood that is this embodiment, the processor 1100 maybe a central processing unit (“CPU” for short). The processor 1100 mayalso be another universal processor, a digital signal processor (DSP),an application-specific integrated circuit (ASIC), a field programmablegate array (FPGA), another programmable logic device, discrete gate,transistor logic device, or discrete hardware assembly, or the like. Theuniversal processor may be a microprocessor, or the processor may alsobe any common processor or the like.

The memory 1200 may be a read-only memory or a random access memory andprovides an instruction and data for the processor 1100. A part of thememory 1200 may further include a non-volatile random access memory. Forexample, the memory 1200 may further store information about devicetypes,

Besides a data bus, the bus system 1300 may further include a powersupply bus, a control bus, a state signal bus, and the like. However,for the convenience of clear description, the various buses areillustrated as the bus system 1300 in the figure.

In an implementation process, the steps of the foregoing methods may becompleted by using an integrated logic circuit of a hardware form or aninstruction of a software form in the processor 1100. The steps withreference to the methods disclosed in the embodiments may be directlycompleted by a hardware processor, or be completed by a combination ofhardware and software modules in the processor. The software module maybe located in a mature storage medium in the art, such as a randomaccess memory, a flash memory, a read-only memory, a programmableread-only memory, an electrically erasable programmable read-onlymemory, or a register. The storage medium is located on the memory 1200,and the processor 1100 completes the steps of the foregoing methods byreading information in the memory 1200 and by using hardware thereof,which is not described herein in detail to avoid repetition.

Optionally, as one embodiment, when the rank determined by the processor1100 is 1, W₂ satisfies the equation (5).

Optionally, as one embodiment, when the rank determined by the processor1100 is 2, W₂ satisfies the equation (6) or the equation (7).

Optionally, as one embodiment, a precoding matrix set corresponding tothe first codebook index corresponding to the first PMI includesprecoding matrices U1 and U2, where the precoding matrices U1 and U2 areindicated by the second codebook index, where:

${{U\; 1} = {\frac{1}{A}\begin{bmatrix}v \\{\beta\; v}\end{bmatrix}}},{{U\; 2} = {\frac{1}{A}\begin{bmatrix}v \\{{- \beta}\; v}\end{bmatrix}}},{v = \begin{bmatrix}1 \\q_{1}^{n + {({8n\mspace{14mu}{mod}\mspace{14mu} 32})}}\end{bmatrix}},$β=j^(└n/4┘)*α(i), i=(n mod 4)+1, α(i)=q₁ ^(2(i-1)), and A is a constant.

Optionally, as one embodiment, when the rank determined by the processor1100 is 1, the precoding matrices W included in the codebook set aredetermined according to Table A.

Optionally, as one embodiment, when the rank determined by the processor1100 is 2, the precoding matrices W included in the codebook set aredetermined according to Table B1 or B2.

Optionally, as one embodiment, when the rank determined by the processor1100 is 1, the first PMI, the second PMI, the first codebook indexcorresponding to the first PMI, and the second codebook indexcorresponding to the second PMI are determined according to Table C1,C2, C3, or C4.

Optionally, as one embodiment, when the rank determined by the processor1100 is 2, the value range of n may be the set {0, 1, 2, 3, 4, 5, 6, 7}or {8, 9, 10, 11, 12, 13, 14, 15}.

In this embodiment, optionally, a value range of the first codebookindex corresponding to the first PMI and a value range of the secondcodebook index corresponding to the second PMI have an associationrelationship. Optionally, that a value range of the first codebook indexcorresponding to the first PMI and a value range of the second codebookindex corresponding to the second PMI have an association relationshipincludes: the value range of the second codebook index corresponding tothe second PMI is uniquely determined according to a value and/or thevalue range of the first codebook index corresponding to the first PMI.

It should be understood that the user equipment 1000 according to thisembodiment may correspond to a user equipment that performs a method fortransmitting a 4-antenna precoding matrix according to an embodiment,and the foregoing and other operations and/or functions of modules inthe user equipment 1000 are used to implement a corresponding procedureof the method in FIG. 1, which is not described herein any further forbrevity.

Therefore, by means of the user equipment according to this embodiment,more precoding matrices that are applicable to a uniform linear arrayantenna may be indicated without changing a feedback mode or feedbackbits, and it may also be ensured that performance for application of adual-polarized antenna is not affected, so that system performance maybe improved and user experience may be enhanced.

As shown in FIG. 14, an embodiment further provides a user equipment2000. The user equipment 2000 includes a processor 2100, a memory 2200,a bus system 2300, and a transmitter 2400. The processor 2100, thememory 2200, and the transmitter 2400 are connected by using the bussystem 2300; the memory 2200 is configured to store an instruction, andthe processor 2100 is configured to execute the instruction stored bythe memory 2200, so as to control the transmitter 2400 to transmit asignal. The processor 2100 is configured to determine a rank used forindicating the number of transmission layers; determine a value of afirst codebook index corresponding to one precoding matrix set in acodebook set, where the codebook set corresponds to the rank, andprecoding matrices included in the codebook set are represented by thefirst codebook index and a second codebook index; and determine ajointly coded value corresponding to the rank and the value of the firstcodebook index, where the jointly coded value and the rank have a firstcorrespondence, and the jointly coded value and the first codebook indexhave a second correspondence. The transmitter 2400 is configured to sendthe jointly coded value to a base station, where the precoding matricesW included in the codebook set satisfy the following equation:

W=W₁×W₂, where

${W_{1} = \begin{bmatrix}X_{n} & 0 \\0 & X_{n}\end{bmatrix}},{X_{n} = \begin{bmatrix}1 & 1 & 1 & 1 \\q_{1}^{n} & q_{1}^{n + 8} & q_{1}^{n + 16} & q_{1}^{n + 24}\end{bmatrix}},$q₁=e^(j2π/32), and n=0, 1, . . . , 15; and

the first codebook index corresponds to one value of n, and a valuerange of n is a set {0, 1, 2, 3, 4, 5, 6, 7}, {8, 9, 10, 11, 12, 13, 14,15}, {0, 2, 4, 6}, {1, 3, 5, 7}, {8, 10, 12, 14}, or {9, 11, 13, 15}.

Therefore, the user equipment according to this embodiment may prevent aproblem where precoding matrices are repeated after subsampling, therebyimproving system performance and enhancing user experience.

Optionally, as one embodiment, when the rank determined by the processor2100 is 1, W₂ satisfies the equation (5).

Optionally, as one embodiment, when the rank determined by the processor2100 is 2, W₂ satisfies the equation (6) or the equation (7).

Optionally, as one embodiment, when the number of bits bearing thejointly coded value is 4, the correspondence between the jointly codedvalue and the rank and the correspondence between the jointly codedvalue and the first codebook index are determined according to Table D.

Optionally, as one embodiment, when the number of bits bearing thejointly coded value is 3, the correspondence between the jointly codedvalue and the rank and the correspondence between the jointly codedvalue and the first codebook index are determined according to Table E.

It should be understood that in this embodiment, when the rank isdetermined to be 1, the precoding matrices W included in the codebookset are determined according to Table A; it should be further understoodthat in this embodiment of the present invention, when the rankdetermined by the UE is 2, the precoding matrices W included in thecodebook set are determined according to Table B1 or B2. It should beunderstood that in this embodiment, the jointly coded value represents avalue generated by performing joint coding on the rank and a first PMI,which is not described herein any further for brevity.

In this embodiment, optionally, a value range of the first codebookindex corresponding to the first PMI and a value range of the secondcodebook index corresponding to a second PMI have an associationrelationship. Optionally, that a value range of the first codebook indexcorresponding to the first PMI and a value range of the second codebookindex corresponding to a second PMI have an association relationshipincludes: the value range of the second codebook index corresponding tothe second PMI is uniquely determined according to a value and/or thevalue range of the first codebook index corresponding to the first PMI.

It should be understood that the user equipment 2000 according to thisembodiment may correspond to a user equipment that performs a method fortransmitting a 4-antenna precoding matrix according to an embodiment,and the foregoing and other operations and/or functions of modules inthe user equipment 2000 are used to implement a corresponding procedureof the method in FIG. 2, which is not described herein any further forbrevity.

Therefore, the user equipment according to this embodiment of thepresent invention may prevent a problem where precoding matrices arerepeated after subsampling, thereby improving system performance andenhancing user experience.

As shown in FIG. 15, an embodiment further provides a user equipment3000. The user equipment 3000 includes a processor 3100, a memory 3200,a bus system 3300, and a transmitter 3400. The processor 3100, thememory 3200, and the transmitter 3400 are connected by using the bussystem 3300; the memory 3200 is configured to store an instruction, andthe processor 3100 is configured to execute the instruction stored bythe memory 3200, so as to control the transmitter 3400 to transmit asignal. The processor 3100 is configured to determine a rank used forindicating the number of transmission layers; determine a firstprecoding matrix in a codebook set corresponding to the rank, whereprecoding matrices included in the codebook set are represented by afirst codebook index and a second codebook index; and determine a secondprecoding matrix indicator PMI used for indicating the first precodingmatrix, where the second PMI and the second codebook index have a firstcorrespondence, and for one given first codebook index, a value range ofthe second codebook index corresponding to a value range of the secondPMI is a proper subset of a value range of the second codebook index.The transmitter 1400 is configured to send the second PMI used forindicating the first precoding matrix to a base station, where theprecoding matrices W included in the codebook set satisfy the followingequation:

W=W₁×W₂, where

${W_{1} = \begin{bmatrix}X_{n} & 0 \\0 & X_{n}\end{bmatrix}},{X_{n} = \begin{bmatrix}1 & 1 & 1 & 1 \\q_{1}^{n} & q_{1}^{n + 8} & q_{1}^{n + 16} & q_{1}^{n + 24}\end{bmatrix}},$q₁=e^(j2π/32), and n=0, 1, . . . , 15; and

the first codebook index corresponds to one value of n, and a valuerange of n is a set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14,15}; when the rank determined by the processor 3100 is 2, in precodingmatrix sets that are determined according to the first codebook indexand the second codebook index corresponding to the value range of thesecond PMI, a first precoding matrix set corresponding to a firstcodebook index i_(1,a) and a second precoding matrix set correspondingto a first codebook index i_(1,a+8) are mutually exclusive, where thefirst codebook index i_(1,a) represents a first codebook indexcorresponding to n whose value is a, the first codebook index i_(1,a+8)represents a first codebook index corresponding to n whose value is a+8,and aε{0, 1, 2, 3, 4, 5, 6, 7}.

Therefore, the user equipment according to this embodiment of thepresent invention may prevent a problem where precoding matrices arerepeated after subsampling, thereby improving system performance andenhancing user experience.

Optionally, as one embodiment, when the rank determined by the processor3100 is 1, W₂ satisfies the equation (5).

Optionally, as one embodiment, when the rank determined by the processor3100 is 2, W₂ satisfies the equation (6) or the equation (7).

Optionally, as one embodiment, when the rank determined by the processor3100 is 2, mutual relationships between the second PMI, the firstcodebook index, and the second codebook index are determined accordingto Table F1 or F2.

Optionally, as one embodiment, when the rank determined by the processor3100 is 3 or 4, the precoding matrices included in the codebook setcorresponding to the rank are: four precoding matrices with codebookindexes 0 to 3 in Table G; four precoding matrices with codebook indexes4 to 7 in Table G; or four precoding matrices with codebook indexes 12to 15 in Table G.

It should be understood that in this embodiment, when the rank isdetermined to be 1, the precoding matrices W included in the codebookset are determined according to Table A; it should be further understoodthat in this embodiment of the present invention, when the rankdetermined by the UE is 2, the precoding matrices W included in thecodebook set are determined according to Table B1 or B2. It should beunderstood that in this embodiment, the jointly coded value represents avalue generated by performing joint coding on the rank and a first PMI,which is not described herein any further for brevity.

In this embodiment, optionally, a value range of the first codebookindex corresponding to the first PMI and the value range of the secondcodebook index corresponding to the second PMI have an associationrelationship. Optionally, that a value range of the first codebook indexcorresponding to the first PMI and the value range of the secondcodebook index corresponding to the second PMI have an associationrelationship includes: the value range of the second codebook indexcorresponding to the second PMI is uniquely determined according to avalue and/or the value range of the first codebook index correspondingto the first PMI.

It should be understood that the user equipment 3000 according to thisembodiment may correspond to a user equipment that performs a method fortransmitting a 4-antenna precoding matrix according to an embodiment,and the foregoing and other operations and/or functions of modules inthe user equipment 3000 are used to implement a corresponding procedureof the method in FIG. 3, which is not described herein any further forbrevity.

Therefore, the user equipment according to this embodiment may prevent aproblem where precoding matrices are repeated after subsampling, therebyimproving system performance and enhancing user experience.

As shown in FIG. 16, an embodiment further provides a base station 6000.The base station 6000 includes a processor 6100, a memory 6200, a bussystem 6300, and a receiver 6400. The processor 6100, the memory 6200,and the receiver 6400 are connected by using the bus system 6300; thememory 6200 is configured to store an instruction, and the processor6100 is configured to execute the instruction stored by the memory 6200,so as to control the receiver 6400 to receive a signal. The receiver6400 is configured to receive a rank used for indicating the number oftransmission layers, a first precoding matrix indicator PMI, and asecond PMI that are sent by a user equipment; the processor 6100 isconfigured to determine a first precoding matrix in a codebook setcorresponding to the rank according to the first PMI and the second PMI,where precoding matrices included in the codebook set are represented bya first codebook index and a second codebook index, the first PMI andthe first codebook index have a first correspondence, and the second PMIand the second codebook index have a second correspondence, where theprecoding matrices W included in the codebook set satisfy the followingequation:

W=W₁×W₂, where

${W_{1} = \begin{bmatrix}X_{n} & 0 \\0 & X_{n}\end{bmatrix}},{X_{n} = \begin{bmatrix}1 & 1 & 1 & 1 \\q_{1}^{n} & q_{1}^{n + 8} & q_{1}^{n + 16} & q_{1}^{n + 24}\end{bmatrix}},$q₁=e^(j2π/32), and n=0, 1, . . . , 15; and

the first codebook index corresponds to one value of n, and a valuerange of n is a set {0, 1, 2, 3, 4, 5, 6, 7}, {8, 9, 10, 11, 12, 13, 14,15}, {0, 2, 4, 6, 8, 10, 12, 14}, or {1, 3, 5, 7, 9, 11, 13, 15}.

Therefore, by means of the base station according to this embodiment,more precoding matrices that are applicable to a uniform linear arrayantenna may be indicated without changing a feedback mode or feedbackbits, and it may also be ensured that performance for application of adual-polarized antenna is not affected, so that system performance maybe improved and user experience may be enhanced.

Optionally, as one embodiment, when the rank determined by the processor6100 is 1, W₂ satisfies the equation (5).

Optionally, as one embodiment, when the rank determined by the processor6100 is 2, W₂ satisfies the equation (6) or the equation (7).

Optionally, as one embodiment, a precoding matrix set corresponding tothe first codebook index corresponding to the first PMI includesprecoding matrices U1 and U2, where the precoding matrices U1 and U2 areindicated by the second codebook index, where:

${{U\; 1} = {\frac{1}{A}\begin{bmatrix}v \\{\beta\; v}\end{bmatrix}}},{{U\; 2} = {\frac{1}{A}\begin{bmatrix}v \\{{- \beta}\; v}\end{bmatrix}}},{v = \begin{bmatrix}1 \\q_{1}^{n + {({8n\mspace{14mu}{mod}\mspace{14mu} 32})}}\end{bmatrix}},$β=j^(└n/4┘)*α(i), i=(n mod 4)+1, α(i)=q₁ ^(2(i-1)), and A is a constant.

Optionally, as one embodiment, when the rank determined by the processor6100 is 1, the precoding matrices W included in the codebook set aredetermined according to Table A.

Optionally, as one embodiment, when the rank determined by the processor6100 is 2, the precoding matrices W included in the codebook set aredetermined according to Table B1 or B2.

Optionally, as one embodiment, when the rank determined by the processor6100 is 1, the first PMI, the second PMI, the first codebook indexcorresponding to the first PMI, and the second codebook indexcorresponding to the second PMI are determined according to Table C1,C2, C3, or C4.

Optionally, as one embodiment, when the rank determined by the processor6100 is 2, the value range of n may be the set {0, 1, 2, 3, 4, 5, 6, 7}or {8, 9, 10, 11, 12, 13, 14, 15}.

In this embodiment, optionally, a value range of the first codebookindex corresponding to the first PMI and a value range of the secondcodebook index corresponding to the second PMI have an associationrelationship. Optionally, that a value range of the first codebook indexcorresponding to the first PMI and a value range of the second codebookindex corresponding to the second PMI have an association relationshipincludes: the value range of the second codebook index corresponding tothe second PMI is uniquely determined according to a value and/or thevalue range of the first codebook index corresponding to the first PMI.

It should be understood that the base station 6000 according to thisembodiment may correspond to a base station that performs a method fortransmitting a 4-antenna precoding matrix according to an embodiment,and the foregoing and other operations and/or functions of modules inthe base station 6000 are used to implement a corresponding procedure ofthe method in FIG. 4, which is not described herein any further forbrevity.

Therefore, by means of the base station according to this embodiment,more precoding matrices that are applicable to a uniform linear arrayantenna may be indicated without changing a feedback mode or feedbackbits, and it may also be ensured that performance for application of adual-polarized antenna is not affected, so that system performance maybe improved and user experience may be enhanced.

As shown in FIG. 17, an embodiment further provides a base station 7000.The base station 7000 includes a processor 7100, a memory 7200, a bussystem 7300, and a receiver 7400. The processor 7100, the memory 7200,and the receiver 7400 are connected by using the bus system 7300; thememory 7200 is configured to store an instruction, and the processor7100 is configured to execute the instruction stored by the memory 7200,so as to control the receiver 7400 to receive a signal. The receiver7400 is configured to receive a jointly coded value sent by a userequipment; the processor 7100 is configured to determine a value of afirst codebook index and a rank used for indicating the number oftransmission layers according to the jointly coded value, acorrespondence between the jointly coded value and the rank and acorrespondence between the jointly coded value and the first codebookindex, where the value of the first codebook index corresponds to oneprecoding matrix set in a codebook set, the codebook set corresponds tothe rank, precoding matrices included in the codebook set arerepresented by the first codebook index and a second codebook index, andthe precoding matrices W included in the codebook set satisfy thefollowing equation:

W=W₁×W₂, where

${W_{1} = \begin{bmatrix}X_{n} & 0 \\0 & X_{n}\end{bmatrix}},{X_{n} = \begin{bmatrix}1 & 1 & 1 & 1 \\q_{1}^{n} & q_{1}^{n + 8} & q_{1}^{n + 16} & q_{1}^{n + 24}\end{bmatrix}},$q₁=e^(j2π/32), and n=0, 1, . . . , 15; and

the first codebook index corresponds to one value of n, and a valuerange of n is a set {0, 1, 2, 3, 4, 5, 6, 7}, {8, 9, 10, 11, 12, 13, 14,15}, {0, 2, 4, 6}, {1, 3, 5, 7}, {8, 10, 12, 14}, or {9, 11, 13, 15}.

Therefore, the base station according to this embodiment may prevent aproblem where precoding matrices are repeated after subsampling, therebyimproving system performance and enhancing user experience.

Optionally, as one embodiment, when the rank determined by the processor7100 is 1, W₂ satisfies the equation (5).

Optionally, as one embodiment, when the rank determined by the processor7100 is 2, W₂ satisfies the equation (6) or the equation (7).

Optionally, as one embodiment, when the number of bits bearing thejointly coded value is 4, the correspondence between the jointly codedvalue and the rank and the correspondence between the jointly codedvalue and the first codebook index are determined according to Table D.

Optionally, as one embodiment, when the number of bits bearing thejointly coded value is 3, the correspondence between the jointly codedvalue and the rank and the correspondence between the jointly codedvalue and the first codebook index are determined according to Table E.

It should be understood that in this embodiment, when the rank isdetermined to be 1, the precoding matrices W included in the codebookset are determined according to Table A; it should be further understoodthat in this embodiment, when the rank determined by the UE is 2, theprecoding matrices W included in the codebook set are determinedaccording to Table B1 or B2. It should be understood that in thisembodiment, the jointly coded value represents a value generated byperforming joint coding on the rank and a first PMI, which is notdescribed herein any further for brevity.

In this embodiment, optionally, a value range of the first codebookindex corresponding to the first PMI and a value range of the secondcodebook index corresponding to a second PMI have an associationrelationship. Optionally, that a value range of the first codebook indexcorresponding to the first PMI and a value range of the second codebookindex corresponding to a second PMI have an association relationshipincludes: the value range of the second codebook index corresponding tothe second PMI is uniquely determined according to the value and/or thevalue range of the first codebook index corresponding to the first PMI.

It should be understood that the base station 7000 according to thisembodiment may correspond to the base station that performs a method fortransmitting a 4-antenna precoding matrix according to an embodiment,and the foregoing and other operations and/or functions of modules inthe base station 7000 are used to implement a corresponding procedure ofthe method in FIG. 5, which is not described herein any further forbrevity.

Therefore, the base station according to this embodiment may prevent aproblem where precoding matrices are repeated after subsampling, therebyimproving system performance and enhancing user experience.

As shown in FIG. 18, an embodiment further provides a base station 8000.The base station 8000 includes a processor 8100, a memory 8200, a bussystem 8300, and a receiver 8400. The processor 8100, the memory 8200,and the receiver 8400 are connected by using the bus system 8300; thememory 8200 is configured to store an instruction, and the processor8100 is configured to execute the instruction stored by the memory 8200,so as to control the receiver 8400 to receive a signal. The receiver8400 is configured to receive a second precoding matrix indicator PMI, afirst codebook index, and a rank used for indicating the number oftransmission layers that are sent by a user equipment; the processor8100 is configured to determine a first precoding matrix in a codebookset corresponding to the rank according to the second PMI and the firstcodebook index, where precoding are included in the codebook set arerepresented by the first codebook index and a second codebook index, thesecond PMI and the second codebook index have a first correspondence,and for one given first codebook index, a value range of the secondcodebook index corresponding to a value range of the second PMI is aproper subset of a value range of the second codebook index, where theprecoding matrices W included in the codebook set satisfy the followingequation:

W=W₁×W₂, where

${W_{1} = \begin{bmatrix}X_{n} & 0 \\0 & X_{n}\end{bmatrix}},{X_{n} = \begin{bmatrix}1 & 1 & 1 & 1 \\q_{1}^{n} & q_{1}^{n + 8} & q_{1}^{n + 16} & q_{1}^{n + 24}\end{bmatrix}},$q₁=e^(j2π/32), and n=0, 1, . . . , 15;

the first codebook index corresponds to one value of n, and a valuerange of n is a set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14,15}; and when the rank received by the receiver 8400 is 2, in precodingmatrix sets that are determined according to the first codebook indexand the second codebook index corresponding to the value range of thesecond PMI, a first precoding matrix set corresponding to a firstcodebook index i_(1,a) and a second precoding matrix set correspondingto a first codebook index i_(1,a+8) are mutually exclusive, where thefirst codebook index i_(1,a) represents a first codebook indexcorresponding to n whose value is a, the first codebook index i_(1,a+8)represents a first codebook index corresponding to n whose value is a+8,and aε{0, 1, 2, 3, 4, 5, 6, 7}.

Therefore, the base station according to this embodiment may prevent aproblem where precoding matrices are repeated after subsampling, therebyimproving system performance and enhancing user experience.

Optionally, as one embodiment, when the rank determined by the processor8100 is 1, W₂ satisfies the equation (5).

Optionally, as one embodiment, when the rank determined by the processor8100 is 2, W₂ satisfies the equation (6) or the equation (7).

Optionally, as one embodiment, when the rank determined by the processor8100 is 2, mutual relationships between the second PMI, the firstcodebook index, and the second codebook index are determined accordingto Table F1 or F2.

Optionally, as one embodiment, when the rank determined by the processor8100 is 3 or 4, the precoding matrices included in the codebook setcorresponding to the rank are: four precoding matrices with codebookindexes 0 to 3 in Table G; four precoding matrices with codebook indexes4 to 7 in Table G; or four precoding matrices with codebook indexes 12to 15 in Table G.

It should be understood that in this embodiment, when the rank isdetermined to be 1, the precoding matrices W included in the codebookset are determined according to Table A; it should be further understoodthat in this embodiment, when the rank determined by the UE is 2, theprecoding matrices W included in the codebook set are determinedaccording to Table B1 or B2. It should be understood that in thisembodiment of the present invention, the jointly coded value representsa value generated by performing joint coding on the rank and a firstPMI, which is not described herein any further for brevity.

In this embodiment, optionally, a value range of the first codebookindex corresponding to the first PMI and the value range of the secondcodebook index corresponding to the second PMI have an associationrelationship. Optionally, that a value range of the first codebook indexcorresponding to the first PMI and the value range of the secondcodebook index corresponding to the second PMI have an associationrelationship includes: the value range of the second codebook indexcorresponding to the second PMI is uniquely determined according to avalue and/or the value range of the first codebook index correspondingto the first PMI.

It should be understood that the base station 8000 according to thisembodiment may correspond to a base station that performs a method fortransmitting a 4-antenna precoding matrix according to an embodiment,and the foregoing and other operations and/or functions of modules inthe base station 8000 are used to implement a corresponding procedure ofthe method in FIG. 6, which is not described herein any further forbrevity.

Therefore, the base station according to this embodiment may prevent aproblem where precoding matrices are repeated after subsampling, therebyimproving system performance and enhancing user experience.

A person of ordinary skill in the art may be aware that, in combinationwith the examples described in the embodiments disclosed in thisspecification, units and algorithm steps may be implemented byelectronic hardware, computer software, or a combination thereof. Toclearly describe the interchangeability between the hardware and thesoftware, the foregoing has generally described compositions and stepsof each example according to functions. Whether the functions areperformed by hardware or software depends on particular applications anddesign constraint conditions of the technical solutions. A personskilled in the art may use different methods to implement the describedfunctions for each particular application, but it should not beconsidered that the implementation goes beyond the scope of the presentinvention.

It may be clearly understood by a person skilled in the art that, forthe purpose of convenient and brief description, for a detailed workingprocess of the foregoing system, apparatus, and unit, reference may bemade to a corresponding process in the foregoing method embodiments, anddetails are not described herein again.

In the several embodiments provided in the present application, itshould be understood that the disclosed system, apparatus, and methodmay be implemented in other manners. For example, the describedapparatus embodiment is merely exemplary. For example, the unit divisionis merely logical function division and may be other division in actualimplementation. For example, a plurality of units or components may becombined or integrated into another system, or some features may beignored or not performed. In addition, the displayed or discussed mutualcouplings or direct couplings or communication connections may beimplemented through some interfaces. The indirect couplings orcommunication connections between the apparatuses or units may beimplemented in electronic, mechanical, or other forms.

The units described as separate parts may or may not be physicallyseparate, and parts displayed as units may or may not be physical units,may be located in one position, or may be distributed on a plurality ofnetwork units. A part or all of the units may be selected according toactual needs to achieve the objectives of the solutions of theembodiments of the present invention.

In addition, functional units in the embodiments of the presentinvention may be integrated into one processing unit, or each of theunits may exist alone physically, or two or more units are integratedinto one unit. The integrated unit may be implemented in a form ofhardware, or may be implemented in a form of a software functional unit.

When the integrated unit is implemented in the form of a softwarefunctional unit and sold or used as an independent product, theintegrated unit may be stored in a computer-readable storage medium.Based on such an understanding, the technical solutions of the presentinvention essentially, or the part contributing to the prior art, or allor a part of the technical solutions may be implemented in the form of asoftware product. The software product is stored in a storage medium andincludes several instructions for instructing a computer device (whichmay be a personal computer, a server, or a network device) to performall or a part of the steps of the methods described in the embodimentsof the present invention. The foregoing storage medium includes: anymedium that can store program code, such as a USB flash drive, aremovable hard disk, a read-only memory (ROM, Read-Only Memory), arandom access memory (RAM, Random Access Memory), a magnetic disk, or anoptical disc.

The foregoing descriptions are merely specific embodiments of thepresent invention, but are not intended to limit the protection scope ofthe present invention. Any modification or replacement readily figuredout by a person skilled in the art within the technical scope disclosedin the present invention shall fall within the protection scope of thepresent invention. Therefore, the protection scope of the presentinvention shall be subject to the protection scope of the claims.

What is claimed is:
 1. A method, comprising: determining a rank used forindicating a number of transmission layers; determining a firstprecoding matrix in a codebook set corresponding to the rank, whereinprecoding matrices comprised in the codebook set are represented by afirst codebook index and a second codebook index; determining a secondprecoding matrix indicator (PMI) for indicating the first precodingmatrix, wherein the second PMI and the second codebook index have afirst correspondence, and for a given first codebook index, a valuerange of the second codebook index corresponding to a value range of thesecond PMI is a proper subset of a value range of the second codebookindex; and sending the second PMI used for indicating the firstprecoding matrix to a base station, wherein: the precoding matrices (W)comprised in the codebook set satisfy the following equation: W=W₁×W₂,wherein ${W_{1} = \begin{bmatrix}X_{n} & 0 \\0 & X_{n}\end{bmatrix}},{X_{n} = \begin{bmatrix}1 & 1 & 1 & 1 \\q_{1}^{n} & q_{1}^{n + 8} & q_{1}^{n + 16} & q_{1}^{n + 24}\end{bmatrix}},$ q₁=e^(j2π/32), and n=0, 1, . . . , 15; wherein thefirst codebook index corresponds to one value of n, and a value range ofn is a set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}; andwherein when the rank is determined to be 2, in precoding matrix setsthat are determined according to the first codebook index and the secondcodebook index corresponding to the value range of the second PMI, afirst precoding matrix set corresponding to a first codebook indexi_(1,a) and a second precoding matrix set corresponding to a firstcodebook index i_(1,a+8) are mutually exclusive, wherein the firstcodebook index i_(1,a) represents a first codebook index correspondingto n whose value is a, the first codebook index i_(1,a+8) represents afirst codebook index corresponding to n whose value is a+8, and aε{0, 1,2, 3, 4, 5, 6, 7}.
 2. The method according to claim 1, wherein when therank is determined to be 1, W₂ satisfies the following equation:${W_{2} \in \left\{ {{\frac{1}{A}\begin{bmatrix}Y \\{{\alpha(i)}Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{j\;{\alpha(i)}Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{{- \alpha}\;(i)Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{{- j}\;{\alpha(i)}Y}\end{bmatrix}}} \right\}},$ wherein Yε{e₁,e₂,e₃,e₄}, α(i)=q₁ ^(2(i-1));when Y is e₁, α(i) is α(1); when Y is e₂, α(i) is α(2); when Y is e₃,α(i) is α(3); when Y is e₄, α(i) is α(4); wherein e_(i) represents acolumn vector with a dimension of 4×1, wherein an i^(th) element ine_(i) is 1, all other elements are 0, and iε{1, 2, 3, 4}; and wherein Ais a constant.
 3. The method according to claim 2, wherein when the rankis determined to be 2, W₂ satisfies the following equation:$\mspace{20mu}{W_{2} \in \left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}} \right\}}$(Y₁, Y₂) ∈ {(e₁, e₁), (e₂, e₂), (e₃, e₃), (e₄, e₄), (e₁, e₂), (e₂, e₃), (e₁, e₄), (e₂, e₄)};  or $W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & Y_{2}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{- Y_{1}} & Y_{2}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{- Y_{1}} & {- Y_{2}}\end{bmatrix}}} \right\}\left( {Y_{1},Y_{2}} \right)} \in {\quad{{\left\{ \left( {e_{2},e_{4}} \right) \right\} W_{2}} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}} \right\}\left( {Y_{1},Y_{2}} \right)} \in {\left\{ {\left( {e_{1},e_{1}} \right),\left( {e_{2},e_{2}} \right),\left( {e_{3},e_{3}} \right),\left( {e_{4},e_{4}} \right)} \right\} W_{2}} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{2} & {- Y_{1}}\end{bmatrix}},} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ {\left( {e_{1},e_{3}} \right),\left( {e_{2},e_{4}} \right),\left( {e_{3},e_{1}} \right),\left( {e_{4},e_{2}} \right)} \right\}}}$wherein e_(i) represents a column vector with a dimension of 4×1, ani^(th) element in e_(i) is 1, all other elements are 0, and iε{1, 2, 3,4}; and wherein B is a constant.
 4. The method according to claim 3,wherein when the rank is determined to be 2, mutual relationshipsbetween the second PMI, the first codebook index, and the secondcodebook index are determined according to Table F1 or F2: TABLE F1I_(PMI2) i₁ i₂ 0-3 0-7  2 × I_(PMI2) 8-15 2 × I_(PMI2) + 1

TABLE F2 I_(PMI2) i₁ i₂ 0-3 0-7 2 × I_(PMI2) 8-15 2 × I_(PMI2) + 8

wherein I_(PMI2) represents the second PMI, i₁ represents the firstcodebook index, and i₂ represents the second codebook index.
 5. Themethod according to claim 1, wherein when the rank is determined to be 3or 4, the precoding matrices comprised in the codebook set correspondingto the rank are: four precoding matrices with codebook indexes 0 to 3 inTable G; or four precoding matrices with codebook indexes 4 to 7 inTable G; or four precoding matrices with codebook indexes 12 to 15 inTable G, TABLE G Codebook RI Index u_(n) 1 2 3 4 0 u₀ = [1 −1 −1 −1]^(T)W₀ ^({1}) W₀ ^({14})/{square root over (2)} W₀ ^({124})/{square rootover (3)} W₀ ^({1234})/2 1 u₁ = [1 −j 1 j]^(T) W₁ ^({1}) W₁^({12})/{square root over (2)} W₁ ^({123})/{square root over (3)} W₁^({1234})/2 2 u₂ = [1 1 −1 1]^(T) W₂ ^({1}) W₂ ^({12})/{square root over(2)} W₂ ^({123})/{square root over (3)} W₂ ^({ 3214})/2 3 u₃ = [1 j 1−j]^(T) W₃ ^({1}) W₃ ^({12})/{square root over (2)} W₃ ^({123})/{squareroot over (3)} W₃ ^({ 3214})/2 4 u₄ = [1 (−1 − j)/{square root over (2)}−j (1 − j)/{square root over (2)}]^(T) W₄ ^({1}) W₄ ^({14})/{square rootover (2)} W₄ ^({124})/{square root over (3)} W₄ ^({1234})/2 5 u₅ = [1 (1− j)/{square root over (2)} j (−1 − j)/{square root over (2)}]^(T) W₅^({1}) W₅ ^({14})/{square root over (2)} W₅ ^({124})/{square root over(3)} W₅ ^({1234})/2 6 u₆ = [1 (1 + j)/{square root over (2)} −j (−1 +j)/{square root over (2)}]^(T) W₆ ^({1}) W₆ ^({13})/{square root over(2)} W₆ ^({134})/{square root over (3)} W₆ ^({1324})/2 7 u₇ = [1 (−1 +j)/{square root over (2)} j (1 + j)/{square root over (2)}]^(T) W₇^({1}) W₇ ^({13})/{square root over (2)} W₇ ^({134})/{square root over(3)} W₇ ^({1324})/2 8 u₈ = [1 −1 1 1]^(T) W₈ ^({1}) W₈ ^({12})/{squareroot over (2)} W₈ ^({124})/{square root over (3)} W₈ ^({1234})/2 9 u₉ =[1 −j −1 −j]^(T) W₉ ^({1}) W₉ ^({14})/{square root over (2)} W₉^({134})/{square root over (3)} W₉ ^({1234})/2 10 u₁₀ = [1 1 1 −1]^(T)W₁₀ ^({1}) W₁₀ ^({13})/{square root over (2)} W₁₀ ^({123})/{square rootover (3)} W₁₀ ^({1324})/2 11 u₁₁ = [1 j −1 j]^(T) W₁₁ ^({1}) W₁₁^({13})/{square root over (2)} W₁₁ ^({134})/{square root over (3)} W₁₁^({1324})/2 12 u₁₂ = [1 −1 −1 1]^(T) W₁₂ ^({1}) W₁₂ ^({12})/{square rootover (2)} W₁₂ ^({123})/{square root over (3)} W₁₂ ^({1234})/2 13 u₁₃ =[1 −1 1 −1]^(T) W₁₃ ^({1}) W₁₃ ^({13})/{square root over (2)} W₁₃^({123})/{square root over (3)} W₁₃ ^({1324})/2 14 u₁₄ = [1 1 −1 −1]^(T)W₁₄ ^({1}) W₁₄ ^({13})/{square root over (2)} W₁₄ ^({123})/{square rootover (3)} W₁₄ ^({ 3214})/2 15 u₁₅ = [1 1 1 1]^(T) W₁₅ ^({1}) W₁₅^({12})/{square root over (2)} W₁₅ ^({123})/{square root over (3)} W₁₅^({1234})/2

wherein W_(n) ^({s}) represents a matrix formed by a column set {s} of amatrix W_(n)=I−2u_(n)u_(n) ^(H)/u_(n) ^(H)u_(n), and I is a 4×4 identitymatrix.
 6. A method, comprising: receiving a second precoding matrixindicator PMI, a first codebook index, and a rank used for indicating anumber of transmission layers that are sent by a user equipment; anddetermining a first precoding matrix in a codebook set corresponding tothe rank according to the second PMI and the first codebook index,wherein precoding matrices comprised in the codebook set are representedby the first codebook index and a second codebook index, the second PMIand the second codebook index have a first correspondence, and for agiven first codebook index, a value range of the second codebook indexcorresponding to a value range of the second PMI is a proper subset of avalue range of the second codebook index; wherein the precoding matricesW comprised in the codebook set satisfy the following equation: W=W₁×W₂,wherein ${W_{1} = \begin{bmatrix}X_{n} & 0 \\0 & X_{n}\end{bmatrix}},{X_{n} = \begin{bmatrix}1 & 1 & 1 & 1 \\q_{1}^{n} & q_{1}^{n + 8} & q_{1}^{n + 16} & q_{1}^{n + 24}\end{bmatrix}},$ q₁=e^(j2π/32), and n=0, 1, . . . , 15; wherein thefirst codebook index corresponds to one value of n, and a value range ofn is a set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}; andwherein when the received rank is 2, in precoding matrix sets that aredetermined according to the first codebook index and the second codebookindex corresponding to the value range of the second PMI, a firstprecoding matrix set corresponding to a first codebook index i_(1,a) anda second precoding matrix set corresponding to a first codebook indexi_(1,a+8) are mutually exclusive, wherein the first codebook indexi_(1,a) represents a first codebook index corresponding to n whose valueis a, and the first codebook index i_(1,a+8) represents a first codebookindex corresponding to n whose value is a+8, and aε{0, 1, 2, 3, 4, 5, 6,7}.
 7. The method according to claim 6, wherein the received rank is 1,and W₂ satisfies the following equation:${W_{2} \in \left\{ {{\frac{1}{A}\begin{bmatrix}Y \\{{\alpha(i)}Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{j\;{\alpha(i)}Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{{- \alpha}\;(i)Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{{- j}\;{\alpha(i)}Y}\end{bmatrix}}} \right\}},$ wherein Yε{e₁,e₂,e₃,e₄}, α(i)=q₁ ^(2(i-1));when Y is e₁, α(i) is α(1); when Y is e₂, α(i) is α(2); when Y is e₃,α(i) is α(3); when Y is e₄, α(i) is α(4); wherein e_(i) represents acolumn vector with a dimension of 4×1, wherein an i^(th) element ine_(i) is 1, all other elements are 0, and iε{1, 2, 3, 4}; and wherein Ais a constant.
 8. The method according to claim 7, wherein the receivedrank is 2, and W₂ satisfies the following equation:$\mspace{20mu}{W_{2} \in \left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}} \right\}}$(Y₁, Y₂) ∈ {(e₁, e₁), (e₂, e₂), (e₃, e₃), (e₄, e₄), (e₁, e₂), (e₂, e₃), (e₁, e₄), (e₂, e₄)};  or $W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & Y_{2}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{- Y_{1}} & Y_{2}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{- Y_{1}} & {- Y_{2}}\end{bmatrix}}} \right\}\left( {Y_{1},Y_{2}} \right)} \in {\quad{{\left\{ \left( {e_{2},e_{4}} \right) \right\} W_{2}} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}} \right\}\left( {Y_{1},Y_{2}} \right)} \in {\left\{ {\left( {e_{1},e_{1}} \right),\left( {e_{2},e_{2}} \right),\left( {e_{3},e_{3}} \right),\left( {e_{4},e_{4}} \right)} \right\} W_{2}} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{2} & {- Y_{1}}\end{bmatrix}},} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ {\left( {e_{1},e_{3}} \right),\left( {e_{2},e_{4}} \right),\left( {e_{3},e_{1}} \right),\left( {e_{4},e_{2}} \right)} \right\}}}$wherein e_(i) represents a column vector with a dimension of 4×1, ani^(th) element in e_(i) is 1, all other elements are 0, and iε{1, 2, 3,4}; B is a constant.
 9. The method according to claim 8, wherein mutualrelationships between the second PMI, the first codebook index, and thesecond codebook index are determined according to Table F1 or F2: TABLEF1 I_(PMI2) i₁ i₂ 0-3 0-7  2 × I_(PMI2) 8-15 2 × I_(PMI2) + 1

TABLE F2 I_(PMI2) i₁ i₂ 0-3 0-7 2 × I_(PMI2) 8-15 2 × I_(PMI2) + 8

wherein I_(PMI2) represents the second PMI, i₁ represents the firstcodebook index, and i₂ represents the second codebook index.
 10. Themethod according to claim 6, wherein the received rank is 3 or 4, andthe precoding matrices comprised in the codebook set corresponding tothe rank are: four precoding matrices with codebook indexes 0 to 3 inTable G; or four precoding matrices with codebook indexes 4 to 7 inTable G; or four precoding matrices with codebook indexes 12 to 15 inTable G, TABLE G Codebook RI Index u_(n) 1 2 3 4 0 u₀ = [1 −1 −1 −1]^(T)W₀ ^({1}) W₀ ^({14})/{square root over (2)} W₀ ^({124})/{square rootover (3)} W₀ ^({1234})/2 1 u₁ = [1 −j 1 j]^(T) W₁ ^({1}) W₁^({12})/{square root over (2)} W₁ ^({123})/{square root over (3)} W₁^({1234})/2 2 u₂ = [1 1 −1 1]^(T) W₂ ^({1}) W₂ ^({12})/{square root over(2)} W₂ ^({123})/{square root over (3)} W₂ ^({ 3214})/2 3 u₃ = [1 j 1−j]^(T) W₃ ^({1}) W₃ ^({12})/{square root over (2)} W₃ ^({123})/{squareroot over (3)} W₃ ^({ 3214})/2 4 u₄ = [1 (−1 − j)/{square root over (2)}−j (1 − j)/{square root over (2)}]^(T) W₄ ^({1}) W₄ ^({14})/{square rootover (2)} W₄ ^({124})/{square root over (3)} W₄ ^({1234})/2 5 u₅ = [1 (1− j)/{square root over (2)} j (−1 − j)/{square root over (2)}]^(T) W₅^({1}) W₅ ^({14})/{square root over (2)} W₅ ^({124})/{square root over(3)} W₅ ^({1234})/2 6 u₆ = [1 (1 + j)/{square root over (2)} −j (−1 +j)/{square root over (2)}]^(T) W₆ ^({1}) W₆ ^({13})/{square root over(2)} W₆ ^({134})/{square root over (3)} W₆ ^({1324})/2 7 u₇ = [1 (−1 +j)/{square root over (2)} j (1 + j)/{square root over (2)}]^(T) W₇^({1}) W₇ ^({13})/{square root over (2)} W₇ ^({134})/{square root over(3)} W₇ ^({1324})/2 8 u₈ = [1 −1 1 1]^(T) W₈ ^({1}) W₈ ^({12})/{squareroot over (2)} W₈ ^({124})/{square root over (3)} W₈ ^({1234})/2 9 u₉ =[1 −j −1 −j]^(T) W₉ ^({1}) W₉ ^({14})/{square root over (2)} W₉^({134})/{square root over (3)} W₉ ^({1234})/2 10 u₁₀ = [1 1 1 −1]^(T)W₁₀ ^({1}) W₁₀ ^({13})/{square root over (2)} W₁₀ ^({123})/{square rootover (3)} W₁₀ ^({1324})/2 11 u₁₁ = [1 j −1 j]^(T) W₁₁ ^({1}) W₁₁^({13})/{square root over (2)} W₁₁ ^({134})/{square root over (3)} W₁₁^({1324})/2 12 u₁₂ = [1 −1 −1 1]^(T) W₁₂ ^({1}) W₁₂ ^({12})/{square rootover (2)} W₁₂ ^({123})/{square root over (3)} W₁₂ ^({1234})/2 13 u₁₃ =[1 −1 1 −1]^(T) W₁₃ ^({1}) W₁₃ ^({13})/{square root over (2)} W₁₃^({123})/{square root over (3)} W₁₃ ^({1324})/2 14 u₁₄ = [1 1 −1 −1]^(T)W₁₄ ^({1}) W₁₄ ^({13})/{square root over (2)} W₁₄ ^({123})/{square rootover (3)} W₁₄ ^({ 3214})/2 15 u₁₅ = [1 1 1 1]^(T) W₁₅ ^({1}) W₁₅^({12})/{square root over (2)} W₁₅ ^({123})/{square root over (3)} W₁₅^({1234})/2

wherein W_(n) ^({s}) represents a matrix formed by a column set {s} of amatrix W_(n)=I−2u_(n)u_(n) ^(H)/u_(n) ^(H)u_(n), and I is a 4×4 identitymatrix.
 11. A user equipment, comprising: a processor, configured to:determine a rank used for indicating a number of transmission layers;determine a first precoding matrix in a codebook set corresponding tothe rank, wherein precoding matrices comprised in the codebook set arerepresented by a first codebook index and a second codebook index;determine a second precoding matrix indicator (PMI) for indicating thefirst precoding matrix, wherein the second PMI and the second codebookindex have a first correspondence, and for a given first codebook index,a value range of the second codebook index corresponding to a valuerange of the second PMI is a proper subset of a value range of thesecond codebook index; and a transmitter, configured to send, to a basestation, the second PMI for indicating the first precoding matrix;wherein the precoding matrices W comprised in the codebook set satisfythe following equation: W=W₁×W₂, wherein ${W_{1} = \begin{bmatrix}X_{n} & 0 \\0 & X_{n}\end{bmatrix}},{X_{n} = \begin{bmatrix}1 & 1 & 1 & 1 \\q_{1}^{n} & q_{1}^{n + 8} & q_{1}^{n + 16} & q_{1}^{n + 24}\end{bmatrix}},$ q₁=e^(j2π/32), and n=0, 1, . . . , 15; wherein thefirst codebook index corresponds to one value of n, and a value range ofn is a set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}; andwherein when the rank determined by the processor is 2, in precodingmatrix sets that are determined according to the first codebook indexand the second codebook index corresponding to the value range of thesecond PMI, a first precoding matrix set corresponding to a firstcodebook index i_(1,a) and a second precoding matrix set correspondingto a first codebook index i_(1,a+8) are mutually exclusive, wherein thefirst codebook index i_(1,a) represents a first codebook indexcorresponding to n whose value is a, the first codebook index i_(1,a+8)represents a first codebook index corresponding to n whose value is a+8,and aε{0, 1, 2, 3, 4, 5, 6, 7}.
 12. The user equipment according toclaim 11, wherein the rank determined by the processor is 1, and W₂satisfies the following equation:${W_{2} \in \left\{ {{\frac{1}{A}\begin{bmatrix}Y \\{{\alpha(i)}Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{j\;{\alpha(i)}Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{{- \alpha}\;(i)Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{{- j}\;{\alpha(i)}Y}\end{bmatrix}}} \right\}},$ wherein Yε{e₁,e₂,e₃,e₄}, α(i)=q₁ ^(2(i-1));when Y is e₁, α(i) is α(1); when Y is e₂, α(i) is α(2); when Y is e₃,α(i) is α(3); when Y is e₄, α(i) is α(4); wherein e_(i) represents acolumn vector with a dimension of 4×1, wherein an i^(th) element ine_(i) is 1, all other elements are 0, and iε{1, 2, 3, 4}; and wherein Ais a constant.
 13. The user equipment according to claim 11, wherein therank determined by the processor is 2, and W₂ satisfies the followingequation: $\mspace{20mu}{W_{2} \in \left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}} \right\}}$(Y₁, Y₂) ∈ {(e₁, e₁), (e₂, e₂), (e₃, e₃), (e₄, e₄), (e₁, e₂), (e₂, e₃), (e₁, e₄), (e₂, e₄)};  or $W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & Y_{2}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{- Y_{1}} & Y_{2}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{- Y_{1}} & {- Y_{2}}\end{bmatrix}}} \right\}\left( {Y_{1},Y_{2}} \right)} \in {\quad{{\left\{ \left( {e_{2},e_{4}} \right) \right\} W_{2}} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}} \right\}\left( {Y_{1},Y_{2}} \right)} \in {\left\{ {\left( {e_{1},e_{1}} \right),\left( {e_{2},e_{2}} \right),\left( {e_{3},e_{3}} \right),\left( {e_{4},e_{4}} \right)} \right\} W_{2}} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{2} & {- Y_{1}}\end{bmatrix}},} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ {\left( {e_{1},e_{3}} \right),\left( {e_{2},e_{4}} \right),\left( {e_{3},e_{1}} \right),\left( {e_{4},e_{2}} \right)} \right\}}}$wherein e_(i) represents a column vector with a dimension of 4×1, ani^(th) element in e_(i) is 1, all other elements are 0, and iε{1, 2, 3,4}; and wherein B is a constant.
 14. The user equipment according toclaim 13, wherein the rank determined by the processor is 2, and mutualrelationships between the second PMI, the first codebook index, and thesecond codebook index are determined according to Table F1 or F2: TABLEF1 I_(PMI2) i₁ i₂ 0-3 0-7  2 × I_(PMI2) 8-15 2 × I_(PMI2) + 1

TABLE F2 I_(PMI2) i₁ i₂ 0-3 0-7 2 × I_(PMI2) 8-15 2 × I_(PMI2) + 8

wherein I_(PMI2) represents the second PMI, i₁ represents the firstcodebook index, and i₂ represents the second codebook index.
 15. Theuser equipment according to claim 11, wherein the rank determined by theprocessor is 3 or 4, and the precoding matrices comprised in thecodebook set corresponding to the rank are: four precoding matrices withcodebook indexes 0 to 3 in Table G; or four precoding matrices withcodebook indexes 4 to 7 in Table G; or four precoding matrices withcodebook indexes 12 to 15 in Table G; TABLE G Codebook RI Index u_(n) 12 3 4 0 u₀ = [1 −1 −1 −1]^(T) W₀ ^({1}) W₀ ^({14})/{square root over(2)} W₀ ^({124})/{square root over (3)} W₀ ^({1234})/2 1 u₁ = [1 −j 1j]^(T) W₁ ^({1}) W₁ ^({12})/{square root over (2)} W₁ ^({123})/{squareroot over (3)} W₁ ^({1234})/2 2 u₂ = [1 1 −1 1]^(T) W₂ ^({1}) W₂^({12})/{square root over (2)} W₂ ^({123})/{square root over (3)} W₂^({ 3214})/2 3 u₃ = [1 j 1 −j]^(T) W₃ ^({1}) W₃ ^({12})/{square rootover (2)} W₃ ^({123})/{square root over (3)} W₃ ^({ 3214})/2 4 u₄ = [1(−1 − j)/{square root over (2)} −j (1 − j)/{square root over (2)}]^(T)W₄ ^({1}) W₄ ^({14})/{square root over (2)} W₄ ^({124})/{square rootover (3)} W₄ ^({1234})/2 5 u₅ = [1 (1 − j)/{square root over (2)} j (−1− j)/{square root over (2)}]^(T) W₅ ^({1}) W₅ ^({14})/{square root over(2)} W₅ ^({124})/{square root over (3)} W₅ ^({1234})/2 6 u₆ = [1 (1 +j)/{square root over (2)} −j (−1 + j)/{square root over (2)}]^(T) W₆^({1}) W₆ ^({13})/{square root over (2)} W₆ ^({134})/{square root over(3)} W₆ ^({1324})/2 7 u₇ = [1 (−1 + j)/{square root over (2)} j (1 +j)/{square root over (2)}]^(T) W₇ ^({1}) W₇ ^({13})/{square root over(2)} W₇ ^({134})/{square root over (3)} W₇ ^({1324})/2 8 u₈ = [1 −1 11]^(T) W₈ ^({1}) W₈ ^({12})/{square root over (2)} W₈ ^({124})/{squareroot over (3)} W₈ ^({1234})/2 9 u₉ = [1 −j −1 −j]^(T) W₉ ^({1}) W₉^({14})/{square root over (2)} W₉ ^({134})/{square root over (3)} W₉^({1234})/2 10 u₁₀ = [1 1 1 −1]^(T) W₁₀ ^({1}) W₁₀ ^({13})/{square rootover (2)} W₁₀ ^({123})/{square root over (3)} W₁₀ ^({1324})/2 11 u₁₁ =[1 j −1 j]^(T) W₁₁ ^({1}) W₁₁ ^({13})/{square root over (2)} W₁₁^({134})/{square root over (3)} W₁₁ ^({1324})/2 12 u₁₂ = [1 −1 −1 1]^(T)W₁₂ ^({1}) W₁₂ ^({12})/{square root over (2)} W₁₂ ^({123})/{square rootover (3)} W₁₂ ^({1234})/2 13 u₁₃ = [1 −1 1 −1]^(T) W₁₃ ^({1}) W₁₃^({13})/{square root over (2)} W₁₃ ^({123})/{square root over (3)} W₁₃^({1324})/2 14 u₁₄ = [1 1 −1 −1]^(T) W₁₄ ^({1}) W₁₄ ^({13})/{square rootover (2)} W₁₄ ^({123})/{square root over (3)} W₁₄ ^({ 3214})/2 15 u₁₅ =[1 1 1 1]^(T) W₁₅ ^({1}) W₁₅ ^({12})/{square root over (2)} W₁₅^({123})/{square root over (3)} W₁₅ ^({1234})/2

wherein W_(n) ^({s}) represents a matrix formed by a column set {s} of amatrix W_(n)=I−2u_(n)u_(n) ^(H)/u_(n) ^(H)u_(n), and I is a 4×4 identitymatrix.
 16. A base station, comprising: a receiver, configured toreceive a second precoding matrix indicator (PMI), a first codebookindex, and a rank used for indicating the number of transmission layersthat are sent by a user equipment; a processor, configured to determine,according to the second PMI and the first codebook index received by thereceiver, a first precoding matrix in a codebook set corresponding tothe rank received by the receiver, wherein precoding matrices comprisedin the codebook set are represented by the first codebook index and asecond codebook index, the second PMI and the second codebook index havea first correspondence, and for a given first codebook index, a valuerange of the second codebook index corresponding to a value range of thesecond PMI is a proper subset of a value range of the second codebookindex; wherein the precoding matrices (W) comprised in the codebook setsatisfy the following equation: W=W₁×W₂, wherein${W_{1} = \begin{bmatrix}X_{n} & 0 \\0 & X_{n}\end{bmatrix}},{X_{n} = \begin{bmatrix}1 & 1 & 1 & 1 \\q_{1}^{n} & q_{1}^{n + 8} & q_{1}^{n + 16} & q_{1}^{n + 24}\end{bmatrix}},$ q₁=e^(j2π/32), and n=0, 1, . . . , 15; wherein thefirst codebook index corresponds to one value of n, and a value range ofn is a set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}; andwherein when the received rank is 2, in precoding matrix sets that aredetermined according to the first codebook index and the second codebookindex corresponding to the value range of the second PMI, a firstprecoding matrix set corresponding to a first codebook index i_(1,a) anda second precoding matrix set corresponding to a first codebook indexi_(1,a+8) are mutually exclusive, wherein the first codebook indexi_(1,a) represents a first codebook index corresponding to n whose valueis a, the first codebook index i_(1,a+8) represents a first codebookindex corresponding to n whose value is a+8, and aε{0, 1, 2, 3, 4, 5, 6,7}.
 17. The base station according to claim 16, wherein the rankreceived by the receiver is 1, and W₂ satisfies the following equation:${W_{2} \in \left\{ {{\frac{1}{A}\begin{bmatrix}Y \\{{\alpha(i)}Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{j\;{\alpha(i)}Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{{- \alpha}\;(i)Y}\end{bmatrix}},{\frac{1}{A}\begin{bmatrix}Y \\{{- j}\;{\alpha(i)}Y}\end{bmatrix}}} \right\}},$ wherein Yε{e₁,e₂,e₃,e₄}, α(i)=q₁ ^(2(i-1));when Y is e₁, α(i) is α(1); when Y is e₂, α(i) is α(2); when Y is e₃,α(i) is α(3); when Y is e₄, α(i) is α(4); wherein e_(i) represents acolumn vector with a dimension of 4×1, wherein an i^(th) element ine_(i) is 1, all other elements are 0, and iε{1, 2, 3, 4}; and wherein Ais a constant.
 18. The base station according to claim 16, wherein therank received by the receiver is 2, and W₂ satisfies the followingequation: $\mspace{20mu}{W_{2} \in \left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}} \right\}}$(Y₁, Y₂) ∈ {(e₁, e₁), (e₂, e₂), (e₃, e₃), (e₄, e₄), (e₁, e₂), (e₂, e₃), (e₁, e₄), (e₂, e₄)};  or $W_{2} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & Y_{2}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{- Y_{1}} & Y_{2}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{- Y_{1}} & {- Y_{2}}\end{bmatrix}}} \right\}\left( {Y_{1},Y_{2}} \right)} \in {\quad{{\left\{ \left( {e_{2},e_{4}} \right) \right\} W_{2}} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}} \right\}\left( {Y_{1},Y_{2}} \right)} \in {\left\{ {\left( {e_{1},e_{1}} \right),\left( {e_{2},e_{2}} \right),\left( {e_{3},e_{3}} \right),\left( {e_{4},e_{4}} \right)} \right\} W_{2}} \in {\left\{ {{\frac{1}{B}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{2} & {- Y_{1}}\end{bmatrix}},} \right\}\left( {Y_{1},Y_{2}} \right)} \in \left\{ {\left( {e_{1},e_{3}} \right),\left( {e_{2},e_{4}} \right),\left( {e_{3},e_{1}} \right),\left( {e_{4},e_{2}} \right)} \right\}}}$wherein e_(i) represents a column vector with a dimension of 4×1, ani^(th) element in e_(i) is 1, all other elements are 0, and iε{1, 2, 3,4}; and wherein B is a constant.
 19. The base station according to claim18, wherein the rank received by the receiver is 2, and mutualrelationships between the second PMI, the first codebook index, and thesecond codebook index are determined according to Table F1 or F2: TABLEF1 I_(PMI2) i₁ i₂ 0-3 0-7  2 × I_(PMI2) 8-15 2 × I_(PMI2) + 1

TABLE F2 I_(PMI2) i₁ i₂ 0-3 0-7 2 × I_(PMI2) 8-15 2 × I_(PMI2) + 8

wherein I_(PMI2) represents the second PMI, i₁ represents the firstcodebook index, and i₂ represents the second codebook index.
 20. Thebase station according to claim 16, wherein the rank received by thereceiver is 3 or 4, the precoding matrices comprised in the codebook setcorresponding to the rank are: four precoding matrices with codebookindexes 0 to 3 in Table G; or four precoding matrices with codebookindexes 4 to 7 in Table G; or four precoding matrices with codebookindexes 12 to 15 in Table G, TABLE G Codebook RI Index u_(n) 1 2 3 4 0u₀ = [1 −1 −1 −1]^(T) W₀ ^({1}) W₀ ^({14})/{square root over (2)} W₀^({124})/{square root over (3)} W₀ ^({1234})/2 1 u₁ = [1 −j 1 j]^(T) W₁^({1}) W₁ ^({12})/{square root over (2)} W₁ ^({123})/{square root over(3)} W₁ ^({1234})/2 2 u₂ = [1 1 −1 1]^(T) W₂ ^({1}) W₂ ^({12})/{squareroot over (2)} W₂ ^({123})/{square root over (3)} W₂ ^({ 3214})/2 3 u₃ =[1 j 1 −j]^(T) W₃ ^({1}) W₃ ^({12})/{square root over (2)} W₃^({123})/{square root over (3)} W₃ ^({ 3214})/2 4 u₄ = [1 (−1 −j)/{square root over (2)} −j (1 − j)/{square root over (2)}]^(T) W₄^({1}) W₄ ^({14})/{square root over (2)} W₄ ^({124})/{square root over(3)} W₄ ^({1234})/2 5 u₅ = [1 (1 − j)/{square root over (2)} j (−1 −j)/{square root over (2)}]^(T) W₅ ^({1}) W₅ ^({14})/{square root over(2)} W₅ ^({124})/{square root over (3)} W₅ ^({1234})/2 6 u₆ = [1 (1 +j)/{square root over (2)} −j (−1 + j)/{square root over (2)}]^(T) W₆^({1}) W₆ ^({13})/{square root over (2)} W₆ ^({134})/{square root over(3)} W₆ ^({1324})/2 7 u₇ = [1 (−1 + j)/{square root over (2)} j (1 +j)/{square root over (2)}]^(T) W₇ ^({1}) W₇ ^({13})/{square root over(2)} W₇ ^({134})/{square root over (3)} W₇ ^({1324})/2 8 u₈ = [1 −1 11]^(T) W₈ ^({1}) W₈ ^({12})/{square root over (2)} W₈ ^({124})/{squareroot over (3)} W₈ ^({1234})/2 9 u₉ = [1 −j −1 −j]^(T) W₉ ^({1}) W₉^({14})/{square root over (2)} W₉ ^({134})/{square root over (3)} W₉^({1234})/2 10 u₁₀ = [1 1 1 −1]^(T) W₁₀ ^({1}) W₁₀ ^({13})/{square rootover (2)} W₁₀ ^({123})/{square root over (3)} W₁₀ ^({1324})/2 11 u₁₁ =[1 j −1 j]^(T) W₁₁ ^({1}) W₁₁ ^({13})/{square root over (2)} W₁₁^({134})/{square root over (3)} W₁₁ ^({1324})/2 12 u₁₂ = [1 −1 −1 1]^(T)W₁₂ ^({1}) W₁₂ ^({12})/{square root over (2)} W₁₂ ^({123})/{square rootover (3)} W₁₂ ^({1234})/2 13 u₁₃ = [1 −1 1 −1]^(T) W₁₃ ^({1}) W₁₃^({13})/{square root over (2)} W₁₃ ^({123})/{square root over (3)} W₁₃^({1324})/2 14 u₁₄ = [1 1 −1 −1]^(T) W₁₄ ^({1}) W₁₄ ^({13})/{square rootover (2)} W₁₄ ^({123})/{square root over (3)} W₁₄ ^({ 3214})/2 15 u₁₅ =[1 1 1 1]^(T) W₁₅ ^({1}) W₁₅ ^({12})/{square root over (2)} W₁₅^({123})/{square root over (3)} W₁₅ ^({1234})/2

wherein W_(n) ^({s}) represents a matrix formed by a column set {s} of amatrix W_(n)=I−2u_(n)u_(n) ^(H)/u_(n) ^(H)u_(n), and I is a 4×4 identitymatrix.